The current article intends to introduce the reader to the concept of injective and projective modules and to describe the CFT. We present a clear view to show the homological algebra and injective and projective modu...The current article intends to introduce the reader to the concept of injective and projective modules and to describe the CFT. We present a clear view to show the homological algebra and injective and projective modules.展开更多
OBJECTIVES: To study the structure specificity of Echinococcus granulosus 95 (Eg95) gene and theopen reading frame (ORF) of the full-length cDNA sequence in Xinjiang, northwestern China andconstruct Eg95 Xinjiang stra...OBJECTIVES: To study the structure specificity of Echinococcus granulosus 95 (Eg95) gene and theopen reading frame (ORF) of the full-length cDNA sequence in Xinjiang, northwestern China andconstruct Eg95 Xinjiang strain DNA vaccine.METHODS: Primers of Eg95 were designed on the basis of the sequence of Eg95 antigen cDNA.Genomic DNA was extracted from E. granulosus protoscoleces (sheep) in Xinjiang. The Eg95 gene andfull-length Eg95 cDNA were amplified by PCR from the genomic DNA and protoscolex cDNA library ofE. granulosus in Xinjiang, respectively. The Eg95 gene was cloned into pUCm-T plasmid and the Eg95cDNA into eukaryotic expression plasmid pcDNA3 for the construction of full-length ORF DNA vaccinepcDNA3-Eg95/XJ. Both Eg95 gene and Eg95 cDNA were sequenced and analyzed by DNAman andNCBI/Blast program.RESULTS: DNA sequence analysis of Eg95 Xinjiang strain (Eg95/XJ) cDNA fragment indicated thatthe coding region of the full-length of Eg95/XJ was 471bp and that encoding a peptide with 156aa and thegenomic DNA size was 1191bp. Homological comparison showed that the ORF of Eg95/XJ cDNA wasidentical to the cDNA sequence of Eg95 reported in the reading frame, but the genomic DNA was anew sequence, named Eg95/XJ and the multiple nucleotide differences, which were represented inEg95/XJ gene in comparison with those of the New Zealand strain, occurred predominantly in thenon-coding regions of the gene. The pcDNA3-Eg95/XJ positive clone was the exact recombinant plasmidand could be used ms a DNA vaccine.CONCLUSION: pcDNA3-Eg95/XJ Xinjiang strain DNA vaccine is successfully constructed.展开更多
A homological multi-information image fusion method was introduced for recognition of the gastric tumor pathological tissue images.The main purpose is that fewer procedures are used to provide more information and the...A homological multi-information image fusion method was introduced for recognition of the gastric tumor pathological tissue images.The main purpose is that fewer procedures are used to provide more information and the result images could be easier to be understood than any other methods.First,multi-scale wavelet transform was used to extract edge feature,and then watershed morphology was used to form multi-threshold grayscale contours.The research laid emphasis upon the homological tissue image fusion based on extended Bayesian algorithm,which fusion result images of linear weighted algorithm was used to compare with the ones of extended Bayesian algorithm.The final fusion images are shown in Fig 5.The final image evaluation was made by information entropy,information correlativity and statistics methods.It is indicated that this method has more advantages for clinical application.展开更多
In 1916, F.S. Macaulay developed specific localization techniques for dealing with “unmixed polynomial ideals” in commutative algebra, transforming them into what he called “inverse systems” of partial differentia...In 1916, F.S. Macaulay developed specific localization techniques for dealing with “unmixed polynomial ideals” in commutative algebra, transforming them into what he called “inverse systems” of partial differential equations. In 1970, D.C. Spencer and coworkers studied the formal theory of such systems, using methods of homological algebra that were giving rise to “differential homological algebra”, replacing unmixed polynomial ideals by “pure differential modules”. The use of “differential extension modules” and “differential double duality” is essential for such a purpose. In particular, 0-pure differential modules are torsion-free and admit an “absolute parametrization” by means of arbitrary potential like functions. In 2012, we have been able to extend this result to arbitrary pure differential modules, introducing a “relative parametrization” where the potentials should satisfy compatible “differential constraints”. We recently noticed that General Relativity is just a way to parametrize the Cauchy stress equations by means of the formal adjoint of the Ricci operator in order to obtain a “minimum parametrization” by adding sufficiently many compatible differential constraints, exactly like the Lorenz condition in electromagnetism. In order to make this difficult paper rather self-contained, these unusual purely mathematical results are illustrated by many explicit examples, two of them dealing with contact transformations, and even strengthening the comments we recently provided on the mathematical foundations of General Relativity and Gauge Theory. They also bring additional doubts on the origin and existence of gravitational waves.展开更多
Considering results obtained in magnetic levitation and suspension of the symmetrical bodies are designed and developed several experiments of the electromagnetism that demonstrate the effects of a superconductor nece...Considering results obtained in magnetic levitation and suspension of the symmetrical bodies are designed and developed several experiments of the electromagnetism that demonstrate the effects of a superconductor necessary to the magnetic levitation/suspension. This generates bases to the development of a reactor to impulse and anti-gravitational magnetic displacement of a vehicle considering the production and transference of Eddy currents on their structure to microscopic level and the effect of auto-levitation/auto-suspension that is obtained with the iso-rotations of the impulse magnetic ring of the proper vehicle.展开更多
This paper proved that graded modules for greded division ring R are graded free modules and R is a IBN ring,and if R is a graded commutative ring,RM is a graded module andRM is a finite semisimple module,then gr.inj....This paper proved that graded modules for greded division ring R are graded free modules and R is a IBN ring,and if R is a graded commutative ring,RM is a graded module andRM is a finite semisimple module,then gr.inj.dimRM=inj.dimRM.展开更多
Let H be a Hopf algebra over a field with bijective antipode, and A a commutative cleft right H-comodule algebra. In this paper, we investigate the ho-mological dimensions and the semisimplicity of the category of rel...Let H be a Hopf algebra over a field with bijective antipode, and A a commutative cleft right H-comodule algebra. In this paper, we investigate the ho-mological dimensions and the semisimplicity of the category of relative Hopf modulesAMH.展开更多
Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left...Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σH, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.展开更多
We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein ...We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.展开更多
In this paper,we introduce the theory of local cohomology and local duality to Notherian connected cochain DG algebras.We show that the notion of the local cohomology functor can be used to detect the Gorensteinness o...In this paper,we introduce the theory of local cohomology and local duality to Notherian connected cochain DG algebras.We show that the notion of the local cohomology functor can be used to detect the Gorensteinness of a homologically smooth DG algebra.For any Gorenstein homologically smooth locally finite DG algebra A,we define a group homomorphism Hdet:Aut_(dg)(A)→k^(×),called the homological determinant.As applications,we present a sufficient condition for the invariant DG subalgebra A^(G)to be Gorenstein,where A is a homologically smooth DG algebra such that H(A)is a Noetherian AS-Gorenstein graded algebra and G is a finite subgroup of Aut_(dg)(A).Especially,we can apply this result to DG down-up algebras and non-trivial DG free algebras generated in two degree-one elements.展开更多
The aim of this paper is two-fold.Given a recollement(T′,T,T′′,i*,i_*,i~!,j!,j*,j*),where T′,T,T′′are triangulated categories with small coproducts and T is compactly generated.First,the authors show that the BB...The aim of this paper is two-fold.Given a recollement(T′,T,T′′,i*,i_*,i~!,j!,j*,j*),where T′,T,T′′are triangulated categories with small coproducts and T is compactly generated.First,the authors show that the BBD-induction of compactly generated t-structures is compactly generated when i*preserves compact objects.As a consequence,given a ladder(T′,T,T′′,T,T′) of height 2,then the certain BBD-induction of compactly generated t-structures is compactly generated.The authors apply them to the recollements induced by homological ring epimorphisms.This is the first part of their work.Given a recollement(D(B-Mod),D(A-Mod),D(C-Mod),i*,i_*,i~!,j!,j*,j_*) induced by a homological ring epimorphism,the last aim of this work is to show that if A is Gorenstein,AB has finite projective dimension and j! restricts to D^b(C-mod),then this recollement induces an unbounded ladder(B-Gproj,A-Gproj,C-Gproj) of stable categories of finitely generated Gorenstein-projective modules.Some examples are described.展开更多
Let H be a finite dimensional cosemisimple Hopf algebra, C a left H-comodule coalgebra and let C = C/C（H^＊）^＋ be the quotient coalgebra and the smash coproduct of C and H. It is shown that if C/C is a eosemisimple...Let H be a finite dimensional cosemisimple Hopf algebra, C a left H-comodule coalgebra and let C = C/C（H^＊）^＋ be the quotient coalgebra and the smash coproduct of C and H. It is shown that if C/C is a eosemisimple coextension and C is an injective right C-comodule, then gl. dim（the smash coproduct of C and H） = gl. dim（C） = gl. dim（C）, where gl. dim（C） denotes the global dimension of coalgebra C.展开更多
We introduce and study （pre）resolving subcategories of a triangulated category and the homological dimension relative to these subcategories. We apply the obtained properties to relative Gorenstein categories.
In this paper,we introduce the notion of excellent extensions of rings.Let F be an excellent extension of an Artin algebra∧,we prove that∧satisfies the Gorenstein symmetry conjecture(resp.,finitistic dimension conje...In this paper,we introduce the notion of excellent extensions of rings.Let F be an excellent extension of an Artin algebra∧,we prove that∧satisfies the Gorenstein symmetry conjecture(resp.,finitistic dimension conjecture,Auslander-Gorenstein conjecture,Nakayama conjecture)if and only if so does F.As a special case of excellent extensions,when G is a finite group whose order is invertible in∧acting on∧and∧is G-stable,we prove that if the skew group algebra∧G satisfies strong Nakayama conjecture(resp.,generalized Nakayama conjecture),then so does∧.展开更多
In Enochs'relative homological dimension theory occur the(co)resolvent and(co)proper dimensions,which are defined by proper and coproper resolutions constructed by precovers and preenvelopes,respectively.Recently,...In Enochs'relative homological dimension theory occur the(co)resolvent and(co)proper dimensions,which are defined by proper and coproper resolutions constructed by precovers and preenvelopes,respectively.Recently,some authors have been interested in relative homological dimensions defined by just exact sequences.In this paper,we contribute to the investigation of these relative homological dimensions.First we study the relation between these two kinds of relative homological dimensions and establish some transfer results under adjoint pairs.Then relative global dimensions are studied,which lead to nice characterizations of some properties of particular cases of self-orthogonal subcategories.At the end of this paper,relative derived functors are studied and generalizations of some known results of balance for relative homology are established.展开更多
Let A be an abelian category,C an additive,full and self-orthogonal subcategory of A closed under direct summands,rG(C)the right Gorenstein subcategory of A relative to C,and⊥C the left orthogonal class of C.For an o...Let A be an abelian category,C an additive,full and self-orthogonal subcategory of A closed under direct summands,rG(C)the right Gorenstein subcategory of A relative to C,and⊥C the left orthogonal class of C.For an object A in A,we prove that if A is in the right 1-orthogonal class of rG(C),then the C-projective and rG(C)-projective dimensions of A are identical;if the rG(C)-projective dimension of A is finite,then the rG(C)-projective and⊥C-projective dimensions of A are identical.We also prove that the supremum of the C-projective dimensions of objects with finite C-projective dimension and that of the rG(C)-projective dimensions of objects with finite rG(C)-projective dimension coincide.Then we apply these results to the category of modules.展开更多
The mitogen-activated protein kinase kinase kinase kinases(MAP4Ks)signaling pathway plays a pivotal role in axonal regrowth and neuronal degeneration following insults.Whether targeting this pathway is beneficial to b...The mitogen-activated protein kinase kinase kinase kinases(MAP4Ks)signaling pathway plays a pivotal role in axonal regrowth and neuronal degeneration following insults.Whether targeting this pathway is beneficial to brain injury remains unclear.In this study,we showed that adeno-associated virus-delivery of the Citron homology domain of MAP4Ks effectively reduces traumatic brain injury-induced reactive gliosis,tauopathy,lesion size,and behavioral deficits.Pharmacological inhibition of MAP4Ks replicated the ameliorative effects observed with expression of the Citron homology domain.Mechanistically,the Citron homology domain acted as a dominant-negative mutant,impeding MAP4K-mediated phosphorylation of the dishevelled proteins and thereby controlling the Wnt/β-catenin pathway.These findings implicate a therapeutic potential of targeting MAP4Ks to alleviate the detrimental effects of traumatic brain injury.展开更多
Reducing the secondary inflammatory response, which is partly mediated by microglia, is a key focus in the treatment of spinal cord injury. Src homology 2-containing protein tyrosine phosphatase 2(SHP2), encoded by PT...Reducing the secondary inflammatory response, which is partly mediated by microglia, is a key focus in the treatment of spinal cord injury. Src homology 2-containing protein tyrosine phosphatase 2(SHP2), encoded by PTPN11, is widely expressed in the human body and plays a role in inflammation through various mechanisms. Therefore, SHP2 is considered a potential target for the treatment of inflammation-related diseases. However, its role in secondary inflammation after spinal cord injury remains unclear. In this study, SHP2 was found to be abundantly expressed in microglia at the site of spinal cord injury. Inhibition of SHP2 expression using siRNA and SHP2 inhibitors attenuated the microglial inflammatory response in an in vitro lipopolysaccharide-induced model of inflammation. Notably, after treatment with SHP2 inhibitors, mice with spinal cord injury exhibited significantly improved hind limb locomotor function and reduced residual urine volume in the bladder. Subsequent in vitro experiments showed that, in microglia stimulated with lipopolysaccharide, inhibiting SHP2 expression promoted M2 polarization and inhibited M1 polarization. Finally, a co-culture experiment was conducted to assess the effect of microglia treated with SHP2 inhibitors on neuronal cells. The results demonstrated that inflammatory factors produced by microglia promoted neuronal apoptosis, while inhibiting SHP2 expression mitigated these effects. Collectively, our findings suggest that SHP2 enhances secondary inflammation and neuronal damage subsequent to spinal cord injury by modulating microglial phenotype. Therefore, inhibiting SHP2 alleviates the inflammatory response in mice with spinal cord injury and promotes functional recovery postinjury.展开更多
Several studies have shown that activation of unfolded protein response and endoplasmic reticulum(ER)stress plays a crucial role in severe cerebral ischemia/reperfusion injury.Autophagy occurs within hours after cereb...Several studies have shown that activation of unfolded protein response and endoplasmic reticulum(ER)stress plays a crucial role in severe cerebral ischemia/reperfusion injury.Autophagy occurs within hours after cerebral ischemia,but the relationship between ER stress and autophagy remains unclear.In this study,we established experimental models using oxygen-glucose deprivation/reoxygenation in PC12 cells and primary neurons to simulate cerebral ischemia/reperfusion injury.We found that prolongation of oxygen-glucose deprivation activated the ER stress pathway protein kinase-like endoplasmic reticulum kinase(PERK)/eukaryotic translation initiation factor 2 subunit alpha(e IF2α)-activating transcription factor 4(ATF4)-C/EBP homologous protein(CHOP),increased neuronal apoptosis,and induced autophagy.Furthermore,inhibition of ER stress using inhibitors or by si RNA knockdown of the PERK gene significantly attenuated excessive autophagy and neuronal apoptosis,indicating an interaction between autophagy and ER stress and suggesting PERK as an essential target for regulating autophagy.Blocking autophagy with chloroquine exacerbated ER stress-induced apoptosis,indicating that normal levels of autophagy play a protective role in neuronal injury following cerebral ischemia/reperfusion injury.Findings from this study indicate that cerebral ischemia/reperfusion injury can trigger neuronal ER stress and promote autophagy,and suggest that PERK is a possible target for inhibiting excessive autophagy in cerebral ischemia/reperfusion injury.展开更多
The sine oculis homeobox homolog(SIX)family,a group of transcription factors characterized by a conserved DNA-binding homology domain,plays a critical role in orchestrating embryonic development and organogenesis acro...The sine oculis homeobox homolog(SIX)family,a group of transcription factors characterized by a conserved DNA-binding homology domain,plays a critical role in orchestrating embryonic development and organogenesis across various organisms,including humans.Comprising six distinct members,from SIX1 to SIX6,each member contributes uniquely to the development and differentiation of diverse tissues and organs,underscoring the versatility of the SIX family.Dysregulation or mutations in SIX genes have been implicated in a spectrum of developmental disorders,as well as in tumor initiation and progression,highlighting their pivotal role in maintaining normal developmental trajectories and cellular functions.Efforts to target the transcriptional complex of the SIX gene family have emerged as a promising strategy to inhibit tumor development.While the development of inhibitors targeting this gene family is still in its early stages,the significant potential of such interventions holds promise for future therapeutic advances.Therefore,this review aimed to comprehensively explore the advancements in understanding the SIX family within gastrointestinal cancers,focusing on its critical role in normal organ development and its implications in gastrointestinal cancers,including gastric,pancreatic,colorectal cancer,and hepatocellular carcinomas.In conclusion,this review deepened the understanding of the functional roles of the SIX family and explored the potential of utilizing this gene family for the diagnosis,prognosis,and treatment of gastrointestinal cancers.展开更多
文摘The current article intends to introduce the reader to the concept of injective and projective modules and to describe the CFT. We present a clear view to show the homological algebra and injective and projective modules.
基金This work was supported by a grant from NIH Project Foundation (No. I-RO-I-TWO-I565-01) and Xinjiang Natural Science Foundation of China (No. 990103003).
文摘OBJECTIVES: To study the structure specificity of Echinococcus granulosus 95 (Eg95) gene and theopen reading frame (ORF) of the full-length cDNA sequence in Xinjiang, northwestern China andconstruct Eg95 Xinjiang strain DNA vaccine.METHODS: Primers of Eg95 were designed on the basis of the sequence of Eg95 antigen cDNA.Genomic DNA was extracted from E. granulosus protoscoleces (sheep) in Xinjiang. The Eg95 gene andfull-length Eg95 cDNA were amplified by PCR from the genomic DNA and protoscolex cDNA library ofE. granulosus in Xinjiang, respectively. The Eg95 gene was cloned into pUCm-T plasmid and the Eg95cDNA into eukaryotic expression plasmid pcDNA3 for the construction of full-length ORF DNA vaccinepcDNA3-Eg95/XJ. Both Eg95 gene and Eg95 cDNA were sequenced and analyzed by DNAman andNCBI/Blast program.RESULTS: DNA sequence analysis of Eg95 Xinjiang strain (Eg95/XJ) cDNA fragment indicated thatthe coding region of the full-length of Eg95/XJ was 471bp and that encoding a peptide with 156aa and thegenomic DNA size was 1191bp. Homological comparison showed that the ORF of Eg95/XJ cDNA wasidentical to the cDNA sequence of Eg95 reported in the reading frame, but the genomic DNA was anew sequence, named Eg95/XJ and the multiple nucleotide differences, which were represented inEg95/XJ gene in comparison with those of the New Zealand strain, occurred predominantly in thenon-coding regions of the gene. The pcDNA3-Eg95/XJ positive clone was the exact recombinant plasmidand could be used ms a DNA vaccine.CONCLUSION: pcDNA3-Eg95/XJ Xinjiang strain DNA vaccine is successfully constructed.
基金Supported by the National Science Foundation of China(No.30370403 )
文摘A homological multi-information image fusion method was introduced for recognition of the gastric tumor pathological tissue images.The main purpose is that fewer procedures are used to provide more information and the result images could be easier to be understood than any other methods.First,multi-scale wavelet transform was used to extract edge feature,and then watershed morphology was used to form multi-threshold grayscale contours.The research laid emphasis upon the homological tissue image fusion based on extended Bayesian algorithm,which fusion result images of linear weighted algorithm was used to compare with the ones of extended Bayesian algorithm.The final fusion images are shown in Fig 5.The final image evaluation was made by information entropy,information correlativity and statistics methods.It is indicated that this method has more advantages for clinical application.
文摘In 1916, F.S. Macaulay developed specific localization techniques for dealing with “unmixed polynomial ideals” in commutative algebra, transforming them into what he called “inverse systems” of partial differential equations. In 1970, D.C. Spencer and coworkers studied the formal theory of such systems, using methods of homological algebra that were giving rise to “differential homological algebra”, replacing unmixed polynomial ideals by “pure differential modules”. The use of “differential extension modules” and “differential double duality” is essential for such a purpose. In particular, 0-pure differential modules are torsion-free and admit an “absolute parametrization” by means of arbitrary potential like functions. In 2012, we have been able to extend this result to arbitrary pure differential modules, introducing a “relative parametrization” where the potentials should satisfy compatible “differential constraints”. We recently noticed that General Relativity is just a way to parametrize the Cauchy stress equations by means of the formal adjoint of the Ricci operator in order to obtain a “minimum parametrization” by adding sufficiently many compatible differential constraints, exactly like the Lorenz condition in electromagnetism. In order to make this difficult paper rather self-contained, these unusual purely mathematical results are illustrated by many explicit examples, two of them dealing with contact transformations, and even strengthening the comments we recently provided on the mathematical foundations of General Relativity and Gauge Theory. They also bring additional doubts on the origin and existence of gravitational waves.
文摘Considering results obtained in magnetic levitation and suspension of the symmetrical bodies are designed and developed several experiments of the electromagnetism that demonstrate the effects of a superconductor necessary to the magnetic levitation/suspension. This generates bases to the development of a reactor to impulse and anti-gravitational magnetic displacement of a vehicle considering the production and transference of Eddy currents on their structure to microscopic level and the effect of auto-levitation/auto-suspension that is obtained with the iso-rotations of the impulse magnetic ring of the proper vehicle.
文摘This paper proved that graded modules for greded division ring R are graded free modules and R is a IBN ring,and if R is a graded commutative ring,RM is a graded module andRM is a finite semisimple module,then gr.inj.dimRM=inj.dimRM.
基金The Fundation of Key Research Program (02021029) and the NSF (2004kj352) of Anhui Province, China.
文摘Let H be a Hopf algebra over a field with bijective antipode, and A a commutative cleft right H-comodule algebra. In this paper, we investigate the ho-mological dimensions and the semisimplicity of the category of relative Hopf modulesAMH.
基金Foundationitem:The NSF(10271081)of Chinathe NSF(1042004)of Beijing City
文摘Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σH, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.
基金supported by National Natural Science Foundation of China(Grant Nos.12061060 and 11801141)Scientific and Technological Planning Project of Yunnan Province(Grant No.202305AC160005)Scientific and Technological Innovation Team of Yunnan Province(Grant No.2020CXTD25)。
文摘We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.
基金supported by National Natural Science Foundation of China (Grant No.11871326)。
文摘In this paper,we introduce the theory of local cohomology and local duality to Notherian connected cochain DG algebras.We show that the notion of the local cohomology functor can be used to detect the Gorensteinness of a homologically smooth DG algebra.For any Gorenstein homologically smooth locally finite DG algebra A,we define a group homomorphism Hdet:Aut_(dg)(A)→k^(×),called the homological determinant.As applications,we present a sufficient condition for the invariant DG subalgebra A^(G)to be Gorenstein,where A is a homologically smooth DG algebra such that H(A)is a Noetherian AS-Gorenstein graded algebra and G is a finite subgroup of Aut_(dg)(A).Especially,we can apply this result to DG down-up algebras and non-trivial DG free algebras generated in two degree-one elements.
文摘The aim of this paper is two-fold.Given a recollement(T′,T,T′′,i*,i_*,i~!,j!,j*,j*),where T′,T,T′′are triangulated categories with small coproducts and T is compactly generated.First,the authors show that the BBD-induction of compactly generated t-structures is compactly generated when i*preserves compact objects.As a consequence,given a ladder(T′,T,T′′,T,T′) of height 2,then the certain BBD-induction of compactly generated t-structures is compactly generated.The authors apply them to the recollements induced by homological ring epimorphisms.This is the first part of their work.Given a recollement(D(B-Mod),D(A-Mod),D(C-Mod),i*,i_*,i~!,j!,j*,j_*) induced by a homological ring epimorphism,the last aim of this work is to show that if A is Gorenstein,AB has finite projective dimension and j! restricts to D^b(C-mod),then this recollement induces an unbounded ladder(B-Gproj,A-Gproj,C-Gproj) of stable categories of finitely generated Gorenstein-projective modules.Some examples are described.
基金Supported by the Foundation of Key Research Program (No. 02021029)the NSF (No. 2004kj352) of Anhui Province, China
文摘Let H be a finite dimensional cosemisimple Hopf algebra, C a left H-comodule coalgebra and let C = C/C（H^＊）^＋ be the quotient coalgebra and the smash coproduct of C and H. It is shown that if C/C is a eosemisimple coextension and C is an injective right C-comodule, then gl. dim（the smash coproduct of C and H） = gl. dim（C） = gl. dim（C）, where gl. dim（C） denotes the global dimension of coalgebra C.
基金Supported by the National Natural Science Foundation of China(Grant No.11571164)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions,Postgraduate Research and Practice Innovation Program of Jiangsu Province(Grant No.KYZZ16 0034)Nanjing University Innovation and Creative Program for PhD candidate(Grant No.2016011)
文摘We introduce and study （pre）resolving subcategories of a triangulated category and the homological dimension relative to these subcategories. We apply the obtained properties to relative Gorenstein categories.
文摘In this paper,we introduce the notion of excellent extensions of rings.Let F be an excellent extension of an Artin algebra∧,we prove that∧satisfies the Gorenstein symmetry conjecture(resp.,finitistic dimension conjecture,Auslander-Gorenstein conjecture,Nakayama conjecture)if and only if so does F.As a special case of excellent extensions,when G is a finite group whose order is invertible in∧acting on∧and∧is G-stable,we prove that if the skew group algebra∧G satisfies strong Nakayama conjecture(resp.,generalized Nakayama conjecture),then so does∧.
基金The second and fourth authors were partially supported by the grant MTM2014-54439-P from Ministerio de Economia y CompetitividadThe third author was partially supported by NSFC(11771202).
文摘In Enochs'relative homological dimension theory occur the(co)resolvent and(co)proper dimensions,which are defined by proper and coproper resolutions constructed by precovers and preenvelopes,respectively.Recently,some authors have been interested in relative homological dimensions defined by just exact sequences.In this paper,we contribute to the investigation of these relative homological dimensions.First we study the relation between these two kinds of relative homological dimensions and establish some transfer results under adjoint pairs.Then relative global dimensions are studied,which lead to nice characterizations of some properties of particular cases of self-orthogonal subcategories.At the end of this paper,relative derived functors are studied and generalizations of some known results of balance for relative homology are established.
基金This research was partially supported by NSFC(Grant Nos.11571164,11971225,11901341)the NSF of Shandong Province(Grant No.ZR2019QA015)。
文摘Let A be an abelian category,C an additive,full and self-orthogonal subcategory of A closed under direct summands,rG(C)the right Gorenstein subcategory of A relative to C,and⊥C the left orthogonal class of C.For an object A in A,we prove that if A is in the right 1-orthogonal class of rG(C),then the C-projective and rG(C)-projective dimensions of A are identical;if the rG(C)-projective dimension of A is finite,then the rG(C)-projective and⊥C-projective dimensions of A are identical.We also prove that the supremum of the C-projective dimensions of objects with finite C-projective dimension and that of the rG(C)-projective dimensions of objects with finite rG(C)-projective dimension coincide.Then we apply these results to the category of modules.
基金supported by the TARCC,Welch Foundation Award(I-1724)the Decherd Foundationthe Pape Adams Foundation,NIH grants NS092616,NS127375,NS117065,NS111776。
文摘The mitogen-activated protein kinase kinase kinase kinases(MAP4Ks)signaling pathway plays a pivotal role in axonal regrowth and neuronal degeneration following insults.Whether targeting this pathway is beneficial to brain injury remains unclear.In this study,we showed that adeno-associated virus-delivery of the Citron homology domain of MAP4Ks effectively reduces traumatic brain injury-induced reactive gliosis,tauopathy,lesion size,and behavioral deficits.Pharmacological inhibition of MAP4Ks replicated the ameliorative effects observed with expression of the Citron homology domain.Mechanistically,the Citron homology domain acted as a dominant-negative mutant,impeding MAP4K-mediated phosphorylation of the dishevelled proteins and thereby controlling the Wnt/β-catenin pathway.These findings implicate a therapeutic potential of targeting MAP4Ks to alleviate the detrimental effects of traumatic brain injury.
基金supported by the Natural Science Research Project of Anhui Province University, No.2023AH040394 (to TY)Hefei Comprehensive National Science Center Leading Medicine and Frontier Technology Research Institute Project, No.2023IHM01073 (to TY)the Natural Science Foundation of Anhui Province, Nos.2308085QH258 (to JW), 2008085MH246 (to TY)。
文摘Reducing the secondary inflammatory response, which is partly mediated by microglia, is a key focus in the treatment of spinal cord injury. Src homology 2-containing protein tyrosine phosphatase 2(SHP2), encoded by PTPN11, is widely expressed in the human body and plays a role in inflammation through various mechanisms. Therefore, SHP2 is considered a potential target for the treatment of inflammation-related diseases. However, its role in secondary inflammation after spinal cord injury remains unclear. In this study, SHP2 was found to be abundantly expressed in microglia at the site of spinal cord injury. Inhibition of SHP2 expression using siRNA and SHP2 inhibitors attenuated the microglial inflammatory response in an in vitro lipopolysaccharide-induced model of inflammation. Notably, after treatment with SHP2 inhibitors, mice with spinal cord injury exhibited significantly improved hind limb locomotor function and reduced residual urine volume in the bladder. Subsequent in vitro experiments showed that, in microglia stimulated with lipopolysaccharide, inhibiting SHP2 expression promoted M2 polarization and inhibited M1 polarization. Finally, a co-culture experiment was conducted to assess the effect of microglia treated with SHP2 inhibitors on neuronal cells. The results demonstrated that inflammatory factors produced by microglia promoted neuronal apoptosis, while inhibiting SHP2 expression mitigated these effects. Collectively, our findings suggest that SHP2 enhances secondary inflammation and neuronal damage subsequent to spinal cord injury by modulating microglial phenotype. Therefore, inhibiting SHP2 alleviates the inflammatory response in mice with spinal cord injury and promotes functional recovery postinjury.
基金supported by the National Natural Science Foundation of China,Nos.82260245(to YX),81660207(to YX),81960253(to YL),82160268(to YL),U1812403(to ZG)Science and Technology Projects of Guizhou Province,Nos.[2019]1440(to YX),[2020]1Z067(to WH)+1 种基金Cultivation Foundation of Guizhou Medical University,No.[20NSP069](to YX)Excellent Young Talents Plan of Guizhou Medical University,No.(2022)101(to WH)。
文摘Several studies have shown that activation of unfolded protein response and endoplasmic reticulum(ER)stress plays a crucial role in severe cerebral ischemia/reperfusion injury.Autophagy occurs within hours after cerebral ischemia,but the relationship between ER stress and autophagy remains unclear.In this study,we established experimental models using oxygen-glucose deprivation/reoxygenation in PC12 cells and primary neurons to simulate cerebral ischemia/reperfusion injury.We found that prolongation of oxygen-glucose deprivation activated the ER stress pathway protein kinase-like endoplasmic reticulum kinase(PERK)/eukaryotic translation initiation factor 2 subunit alpha(e IF2α)-activating transcription factor 4(ATF4)-C/EBP homologous protein(CHOP),increased neuronal apoptosis,and induced autophagy.Furthermore,inhibition of ER stress using inhibitors or by si RNA knockdown of the PERK gene significantly attenuated excessive autophagy and neuronal apoptosis,indicating an interaction between autophagy and ER stress and suggesting PERK as an essential target for regulating autophagy.Blocking autophagy with chloroquine exacerbated ER stress-induced apoptosis,indicating that normal levels of autophagy play a protective role in neuronal injury following cerebral ischemia/reperfusion injury.Findings from this study indicate that cerebral ischemia/reperfusion injury can trigger neuronal ER stress and promote autophagy,and suggest that PERK is a possible target for inhibiting excessive autophagy in cerebral ischemia/reperfusion injury.
基金Supported by the National Natural Science Foundation of China,No.82273457the Natural Science Foundation of Guangdong Province,No.2023A1515012762 and No.2021A1515010846+1 种基金Special Grant for Key Area Programs of Guangdong Department of Education,No.2021ZDZX2040Science and Technology Special Project of Guangdong Province,No.210715216902829.
文摘The sine oculis homeobox homolog(SIX)family,a group of transcription factors characterized by a conserved DNA-binding homology domain,plays a critical role in orchestrating embryonic development and organogenesis across various organisms,including humans.Comprising six distinct members,from SIX1 to SIX6,each member contributes uniquely to the development and differentiation of diverse tissues and organs,underscoring the versatility of the SIX family.Dysregulation or mutations in SIX genes have been implicated in a spectrum of developmental disorders,as well as in tumor initiation and progression,highlighting their pivotal role in maintaining normal developmental trajectories and cellular functions.Efforts to target the transcriptional complex of the SIX gene family have emerged as a promising strategy to inhibit tumor development.While the development of inhibitors targeting this gene family is still in its early stages,the significant potential of such interventions holds promise for future therapeutic advances.Therefore,this review aimed to comprehensively explore the advancements in understanding the SIX family within gastrointestinal cancers,focusing on its critical role in normal organ development and its implications in gastrointestinal cancers,including gastric,pancreatic,colorectal cancer,and hepatocellular carcinomas.In conclusion,this review deepened the understanding of the functional roles of the SIX family and explored the potential of utilizing this gene family for the diagnosis,prognosis,and treatment of gastrointestinal cancers.
