Amply socle supplemented modules

Abstract

In this work, amply socle supplemented modules are defined and some properties of these modules are investigated. We prove that every π− projective and socle supplemented module is amply socle supplemented. We also prove that every factor module and every homomorphic image of an amply socle supplemented module are amply socle supplemented. Let M be a projective and socle supplemented R−module. Then every finitely M−generated R−module is amply socle supplemented.