Abstract
The main objective of this paper is investigating centrally (quasi-)morphic modules as a generalization of centrally morphic rings. We call an R-module M centrally quasi-morphic if for any f ∈ End R ( M ) , there exist central elements g , h ∈ End R ( M ) such that Ker f = Im g and Im f = Ker h . In addition, MR is said to be centrally morphic whenever g = h in the above definition. We show that for image-projective modules, these two notions coincide and every centrally quasi-morphic module is abelian. We prove that a module with strongly regular endomorphism ring (called strongly endoregular) is centrally morphic. Several properties of strongly endoregular modules are obtained.
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