Generalizations of $ss$-supplemented modules
| Autor: | I. Soydan, E. Türkmen |
|---|---|
| Jazyk: | English<br />Ukrainian |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Karpatsʹkì Matematičnì Publìkacìï, Vol 13, Iss 1, Pp 119-126 (2021) |
| Druh dokumentu: | article |
| ISSN: | 2075-9827 2313-0210 |
| DOI: | 10.15330/cmp.13.1.119-126 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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