TY - JOUR
AU - Soydan, I.
AU - TÃ¼rkmen, E.
PY - 2021/06/16
Y2 - 2024/04/19
TI - Generalizations of $ss$-supplemented modules
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 13
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.13.1.119-126
UR - https://scijournals.pnu.edu.ua/index.php/cmp/article/view/3948
SP - 119-126
AB - <p>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.</p>
ER -