Let R be an associative ring not necessarily possessing an identity and （S,≤） a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having pr...Let R be an associative ring not necessarily possessing an identity and （S,≤） a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having property （F）.It is shown that M is a co-Hopfian left R-module if and only if [M<sup>S,≤</sup>]is a co-Hopfan left [[R<sup>S,≤</sup>]]-module.展开更多
The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo...The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo injective modules. Various results are devel- oped, many extending known results. As applications, we give some characterizations on Noetherian rings, QI rings, quasi-Frobenius rings.展开更多
In this paper, we study the closeness of strongly （∞）-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if M[...In this paper, we study the closeness of strongly （∞）-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if M[X] is strongly hopfian （resp. strongly co-hopfian） in R[X]-Mod, then M is strongly hopfian （resp. strongly co-hopfian） in R-Mod.展开更多
基金Research supported by National Natural Science Foundation of China,19671063
文摘Let R be an associative ring not necessarily possessing an identity and （S,≤） a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having property （F）.It is shown that M is a co-Hopfian left R-module if and only if [M<sup>S,≤</sup>]is a co-Hopfan left [[R<sup>S,≤</sup>]]-module.
基金Supported by the Ph.D.Programs Foundation of Ministry of Education of China(200803570003)
文摘The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo injective modules. Various results are devel- oped, many extending known results. As applications, we give some characterizations on Noetherian rings, QI rings, quasi-Frobenius rings.
基金Supported by National Natural Science Foundation of China (Grant No. 10961021)
文摘In this paper, we study the closeness of strongly （∞）-hopfian properties under some constructions such as the ring of Morita context, direct products, triangular matrix, fraction ring etc. Also, we prove that if M[X] is strongly hopfian （resp. strongly co-hopfian） in R[X]-Mod, then M is strongly hopfian （resp. strongly co-hopfian） in R-Mod.
