Generalizations of $ss$-supplemented modules

Keywords: semisimple module, (strongly) $ss$-radical supplemented module, $WV$-rings
Published online: 2021-06-16


We introduce the concept of (strongly) $ss$-radical supplemented modules. We prove that if a submodule $N$ of $M$ is strongly $ss$-radical supplemented and $Rad(M/N)=M/N$, then $M$ is strongly $ss$-radical supplemented. For a left good ring $R$, we show that $Rad(R)\subseteq Soc(_{R}R)$ if and only if every left $R$-module is $ss$-radical supplemented. We characterize the rings over which all modules are strongly $ss$-radical supplemented. We also prove that over a left $WV$-ring every supplemented module is $ss$-supplemented.

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How to Cite
Soydan I., Türkmen E. Generalizations of $ss$-Supplemented Modules. Carpathian Math. Publ. 2021, 13 (1), 119-126.