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- W2990293088 abstract "A left module $M$ over an arbitrary ring is called an $mathcal{RD}$-module (or an $mathcal{RS}$-module) if every submodule $N$ of $M$ with ${rm Rad}(M)subseteq N$ is a direct summand of (a supplement in, respectively) $M$. In this paper, we investigate the various properties of $mathcal{RD}$-modules and $mathcal{RS}$-modules. We prove that $M$ is an $mathcal{RD}$-module if and only if $M={rm Rad}(M)oplus X$, where $X$ is semisimple. We show that a finitely generated $mathcal{RS}$-module is semisimple. This gives us the characterization of semisimple rings in terms of $mathcal{RS}$-modules. We completely determine the structure of these modules over Dedekind domains." @default.
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- W2990293088 date "2019-11-25" @default.
- W2990293088 modified "2023-09-23" @default.
- W2990293088 title "A note on generalizations of semisimple modules" @default.
- W2990293088 doi "https://doi.org/10.14712/1213-7243.2019.011" @default.
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