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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Veröffentlicht in:Communications in algebra Jg. 53; H. 4; S. 1365 - 1377
Hauptverfasser: Dehghani, Najmeh, Sedaghatjoo, Mojtaba
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Abingdon Taylor & Francis 03.04.2025
Taylor & Francis Ltd
Schlagworte:
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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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2024.2409328