Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3374
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.
Keywords
$ss$-Supplement, radical-s-projective modules, endomorphism rings
First Page
502
Last Page
515
Recommended Citation
KIR, EMİNE ÖNAL
(2023)
"A note on $ss$-supplement submodules,"
Turkish Journal of Mathematics: Vol. 47:
No.
2, Article 6.
https://doi.org/10.55730/1300-0098.3374
Available at:
https://journals.tubitak.gov.tr/math/vol47/iss2/6
