对于具有性质“每个元都适合方程x^2=e”的一类群,其构造如何呢?本文我们将给出它的构造,并得出一些结果。其中,定理2是IRVING KAPLANSKY《INFINITE ABELI AN GROUPS》中定理6的一个特殊情况,但我们用的是另一种证法,首先我们指出: 引...对于具有性质“每个元都适合方程x^2=e”的一类群,其构造如何呢?本文我们将给出它的构造,并得出一些结果。其中,定理2是IRVING KAPLANSKY《INFINITE ABELI AN GROUPS》中定理6的一个特殊情况,但我们用的是另一种证法,首先我们指出: 引理1 若群G的每个元都适合方程x^2=e,则G是交换群。展开更多
Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi ar...Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.展开更多
Let R be a commutative ring with an identity element, G a finitely generated abelian group. In this paper,we investigate necessary and sufficient conditions on G and R such that every finitely generated projective RG ...Let R be a commutative ring with an identity element, G a finitely generated abelian group. In this paper,we investigate necessary and sufficient conditions on G and R such that every finitely generated projective RG module can be extended from R.展开更多
Many of people have tried to obtain the structure of Baer-invariant of groups exactly. Recently, B. Mashayekhy and M. Parvizi determine Baer-invariant of finitely generated Abelian groups. Also, it is done for some no...Many of people have tried to obtain the structure of Baer-invariant of groups exactly. Recently, B. Mashayekhy and M. Parvizi determine Baer-invariant of finitely generated Abelian groups. Also, it is done for some non-Abelian groups, such the dihedral and the quaternion groups directly, and sometimes with the softwares of Gap and Magma. But nobody works on non finitely generated Abelian groups. In 1979, M.R.R. Moghaddarn showed that the structure of Baer-invariant of group commutes with the direct limit of a directed system, in some sense. The authors have used these results and proved that the Baer-invariant of C is always trivial and also Baer-invariant of Abelian groups Q/z and Z （p∞）, with respect to the varieties of outer commutators and so polynilpotent, nilpotent are trivial. One can see immediately that the covering groups of these groups are themselves. Then after computing the Baer-invariant of Zn with respect to Burnside variety, we have concluded for Q/z and Z（P∞） Burnside variety. In the future, they try to survey the commutativity of the Baer-invariant variety with the other useful varieties in order to attain similar results for another non finitely generated Abelian groups.展开更多
In this paper, it is shown that for a QF ring R, the category of projectiveleft R-modules is a category with factorization if and only if gl.dim R ≤1, moreover, ifP(RR) = P(RR) = O,then the meta-Grothendieck groups o...In this paper, it is shown that for a QF ring R, the category of projectiveleft R-modules is a category with factorization if and only if gl.dim R ≤1, moreover, ifP(RR) = P(RR) = O,then the meta-Grothendieck groups obtained by left modules orby right modules are the same, up to isomorphism. It is also shown that the category of f.g. meta-pojective left R-modules is not only a category with factorization but also acategory with product such that it has a small skeletal subcategory.展开更多
Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the ...Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups:Tori[[ RS,≤]]([[MS,≤]],[NS,≤])≌ s∈S ToriR (M,N).展开更多
Let F be a finitely generated free group. Martino and Ventura gave an explicit description for the fixed subgroups of automorphisms of F. The author generalizes their results to injective endomorphisms.
文摘对于具有性质“每个元都适合方程x^2=e”的一类群,其构造如何呢?本文我们将给出它的构造,并得出一些结果。其中,定理2是IRVING KAPLANSKY《INFINITE ABELI AN GROUPS》中定理6的一个特殊情况,但我们用的是另一种证法,首先我们指出: 引理1 若群G的每个元都适合方程x^2=e,则G是交换群。
基金Climb-Up (Pan Deng) Project of Department of Science and Technology of China，国家自然科学基金，Doctoral Programme Foundation of Institution of Higher Education of China
文摘Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.
文摘Let R be a commutative ring with an identity element, G a finitely generated abelian group. In this paper,we investigate necessary and sufficient conditions on G and R such that every finitely generated projective RG module can be extended from R.
文摘Many of people have tried to obtain the structure of Baer-invariant of groups exactly. Recently, B. Mashayekhy and M. Parvizi determine Baer-invariant of finitely generated Abelian groups. Also, it is done for some non-Abelian groups, such the dihedral and the quaternion groups directly, and sometimes with the softwares of Gap and Magma. But nobody works on non finitely generated Abelian groups. In 1979, M.R.R. Moghaddarn showed that the structure of Baer-invariant of group commutes with the direct limit of a directed system, in some sense. The authors have used these results and proved that the Baer-invariant of C is always trivial and also Baer-invariant of Abelian groups Q/z and Z （p∞）, with respect to the varieties of outer commutators and so polynilpotent, nilpotent are trivial. One can see immediately that the covering groups of these groups are themselves. Then after computing the Baer-invariant of Zn with respect to Burnside variety, we have concluded for Q/z and Z（P∞） Burnside variety. In the future, they try to survey the commutativity of the Baer-invariant variety with the other useful varieties in order to attain similar results for another non finitely generated Abelian groups.
基金Supported by the National Natural Science Foundation of China(1990100),theNatural Science Foundation of Guangdong Province.
文摘In this paper, it is shown that for a QF ring R, the category of projectiveleft R-modules is a category with factorization if and only if gl.dim R ≤1, moreover, ifP(RR) = P(RR) = O,then the meta-Grothendieck groups obtained by left modules orby right modules are the same, up to isomorphism. It is also shown that the category of f.g. meta-pojective left R-modules is not only a category with factorization but also acategory with product such that it has a small skeletal subcategory.
基金the National Natural Science Foundation of China (No.10961021)the Teaching and Research Award Program for Outsanding Young Teachers in Higher Education Institutions of Ministry of Education(No.NCET-02-080)
文摘Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups:Tori[[ RS,≤]]([[MS,≤]],[NS,≤])≌ s∈S ToriR (M,N).
基金supported by the National Natural Science Foundation of China(No.11201364)
文摘Let F be a finitely generated free group. Martino and Ventura gave an explicit description for the fixed subgroups of automorphisms of F. The author generalizes their results to injective endomorphisms.
