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- Title
Coretractable modules relative to a module.
- Authors
Beiranvand, P. Karimi; Beyranvand, R.
- Abstract
In this paper, we introduce and study a generalization of coretractable modules. An R -module M is called coretractable relative to an R-module N if Hom R (M / X , N) ≠ 0 , for any proper submodule X of M. It is shown that a right R -module M is coretractable relative to ⊕ i ∈ I N i if and only if M is coretractable relative to N i , for some i ∈ I. Also we show that if R is a right quasi-duo ring, then there exists a right R -module that it is coretractable relative to N , for any nonzero right R -module N if and only if R is a left perfect local ring.
- Subjects
ENDOMORPHISM rings; MODULES (Algebra); LOCAL rings (Algebra); GENERALIZATION
- Publication
Journal of Algebra & Its Applications, 2024, Vol 23, Issue 5, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498824501032