A generalization of semiperfect modules - Türkmen, B. N. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
A module $M$ is called radical semiperfect, if $\frac MN$ has a projective cover whenever $Rad(M) \subseteq N \subseteq M$. 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.