On Proper Class Coprojectively Generated by Modules With Projective Socle

Abstract

Let $\varepsilon$ : 0 --> A -->f B -->g C --> 0 be a short exact sequence of modules and module homomorphism. $\varepsilon$ is called gd-closed sequence if Imf is gd-closed in B. In this paper, the proper class $GD$− Closed, which is coprojectively generated by modules with projective socle, be studied and also its relations among Neat, Closed, $D$−Closed, $S$−Closed be investigated. Additionally, we examine coprojective modules of this class. .