Centrally (quasi-)morphic modules

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...

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Vydané v:	Communications in algebra Ročník 53; číslo 4; s. 1365 - 1377
Hlavní autori:	Dehghani, Najmeh, Sedaghatjoo, Mojtaba
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Abingdon Taylor & Francis 03.04.2025 Taylor & Francis Ltd
Predmet:	Abelian module centrally morphic module centrally quasi-morphic module finitely cogenerated module image-projective module Modules
ISSN:	0092-7872, 1532-4125
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Popis
Shrnutí:	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, M R 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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0092-7872 1532-4125
DOI:	10.1080/00927872.2024.2409328