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.

Keywords

• Hopfian module
• generalized Hopfian module
• e-small submodule
• e-gH module.