2017
Том 69
№ 9

All Issues

A generalization of semiperfect modules

Türkmen B. N.


Abstract

A module $M$ is called radical semiperfect, if $\frac MN$ has a projective cover whenever $\mathrm{R}\mathrm{a}\mathrm{d}(M) \subseteq N \subseteq M$. We study various properties of these modules. It is proved that every left $R$-module is radical semiperfect if and only if $R$ is left perfect. Moreover, radical lifting modules are defined as a generalization of lifting modules.

Citation Example: Türkmen B. N. A generalization of semiperfect modules // Ukr. Mat. Zh. - 2017. - 69, № 1. - pp. 104-112.