Purely co-Hopfian Modules

Abstract

Let R be an associative ring with identity and M a non – zero unitary R-module.In this paper we introduce the definition of purely co-Hopfian module, where an R-module M is said to be purely co-Hopfian if for any monomorphism f ˛ End (M), Imf is pure in M and we give some properties of this kind of modules.

Keywords

• co-Hopfian module, semi co-Hopfian module, purely co-Hopfian module