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Keywords
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Abelian module, centrally morphic module, centrally quasi-morphic module, finitely cogenerated module, image-projective module.
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Abstract
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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.
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