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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| Published in: | Communications in algebra Vol. 53; no. 4; pp. 1365 - 1377 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Abingdon
Taylor & Francis
03.04.2025
Taylor & Francis Ltd |
| Subjects: | |
| ISSN: | 0092-7872, 1532-4125 |
| Online Access: | Get full text |
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| Summary: | 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. |
|---|---|
| Bibliography: | 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 |