Najmeh Dehghani

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 ∈ EndR(M), there exist central elements g, h ∈ EndR(M) such that Kerf = Img and Imf = Kerh. 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-morphicmoduleisabelian.Weprovethatamodulewithstronglyregular endomorphism ring (called strongly endoregular) is centrally morphic. Several properties of strongly endoregular modules are obtained.