As a generalization of power series rings, Ribenboim introduced the notion of the rings of generalized power series. Let R be a commutative ring, and （S.≤） a strictly totally ordered monoid. We prove that （1） the...As a generalization of power series rings, Ribenboim introduced the notion of the rings of generalized power series. Let R be a commutative ring, and （S.≤） a strictly totally ordered monoid. We prove that （1） the ring [[R<sup>(</sup>S.≤]] of generalized power series is a PP-ring if and only if R is a PP-ring and every S-indexed subset C of B（R） （the set of all idempotents of R） has a least upper bound in B（R）. and （2） if （S. ≤） also satisfies the condition that 0≤s for any s∈S, then the ring [[R<sup>(</sup>S.≤]] is weakly PP if and only if R is weakly PP.展开更多
In this paper we characterize semirings all of whose p-injective semimodules are injective. We also classify monoids all of whose p-injective acts are injective.
基金Research supported by National Natural Science Foundation of China. 19501007Natural Science Foundation of Gansu. ZQ-96-01
文摘As a generalization of power series rings, Ribenboim introduced the notion of the rings of generalized power series. Let R be a commutative ring, and （S.≤） a strictly totally ordered monoid. We prove that （1） the ring [[R<sup>(</sup>S.≤]] of generalized power series is a PP-ring if and only if R is a PP-ring and every S-indexed subset C of B（R） （the set of all idempotents of R） has a least upper bound in B（R）. and （2） if （S. ≤） also satisfies the condition that 0≤s for any s∈S, then the ring [[R<sup>(</sup>S.≤]] is weakly PP if and only if R is weakly PP.
基金The second author is supported by National Natural Science Foundation of China （Grant No. 10961021） and the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China Acknowledgements The authors wish to express their sincere thanks to the referees for their valuable suggestions.
文摘In this paper we characterize semirings all of whose p-injective semimodules are injective. We also classify monoids all of whose p-injective acts are injective.
