科研之友
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摘要
A module M is called epi-retractable if every submodule of M is a homomorphic image of M. Dually, a module M is called co-epi-retractable if it contains a copy of each of its factor modules. In special case, a ring R is called co-ph (respectively, copri) if RR (respectively, RR) is co-epi-retractable. It is proved that if R is a left principal right duo ring, then every left ideal of R is an epi-retractable R-module. A co-ph strongly prime ring R is a simple ring. A left self-injective co-ph ring R is left Noetherian if and only if R is a left perfect ring. It is shown that a cogenerator ring R is a ph ring if and only if it is a co-pri ring. Moreover, if R is a left perfect ring such that every projective R-module is co-epi-retractable, then R is a quasi-Frobenius ring.
- 出版日期2013-10
