Modules in which every surjective endomorphism has an e-small kernel

Abstract

In this paper we introduce the notion of e-gH modules which is a proper generalization of Hopfian modules and defined as, a module  is called e-gH if, any surjective -endomorphism  of  has an e-small kernel, a ring  is called e-gH if,  is e-gH. We give some characterizations and properties of this modules.