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Turkish Journal of Mathematics

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 $End_{R}(P)$. 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.

DOI

10.55730/1300-0098.3374

Keywords

$ss$-Supplement, radical-s-projective modules, endomorphism rings

First Page

502

Last Page

515

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