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- Title
A note on ss-supplement submodules.
- Authors
ÖNAL KIR, Emine
- Abstract
In this paper, we describe ss-supplement submodules in terms of a special class of endomorphisms. Let R be a ring with semisimple radical and P be a projective R-module. We show that there is a bijection between ss-supplement submodules of P and ss-supplement submodules of EndR(P) . Moreover, we define radical-s-projective modules as a generalization of projective modules. We prove that every ss-supplement submodule of a projective R-module is radical-s-projective over the ring R with semisimple radical. We show that over SSI -ring R, every radical-s-projective R-module is projective. We provide that over a ring R with semisimple radical, every ss-supplement submodule of a projective R-module is a direct summand if and only if every radical-s-projective R-module is projective.
- Subjects
ENDOMORPHISM rings; SEMISIMPLE Lie groups; ENDOMORPHISMS; BIJECTIONS
- Publication
Turkish Journal of Mathematics, 2023, Vol 47, Issue 2, p502
- ISSN
1300-0098
- Publication type
Article
- DOI
10.55730/1300-0098.3374