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
In this paper we study some properties of the Hurwitz series ring HA over a commutative ring A, such as the nilradical of HA and the chain condition on its an- nihilators. We provide an example showing that the last p...In this paper we study some properties of the Hurwitz series ring HA over a commutative ring A, such as the nilradical of HA and the chain condition on its an- nihilators. We provide an example showing that the last property does not pass from A to HA. A strongly Hopfian ring is a ring satisfying the chain condition on some type of annihilators. We give a large class of strongly Hopfian rings A such that HA are not strongly Hopfian.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.
文摘In this paper we study some properties of the Hurwitz series ring HA over a commutative ring A, such as the nilradical of HA and the chain condition on its an- nihilators. We provide an example showing that the last property does not pass from A to HA. A strongly Hopfian ring is a ring satisfying the chain condition on some type of annihilators. We give a large class of strongly Hopfian rings A such that HA are not strongly Hopfian.
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.
