- Hacettepe Journal of Mathematics and Statistics
- Vol: 47 Issue: 6
- $\oplus$-co-coatomically supplemented and co-coatomically semiperfect modules
$\oplus$-co-coatomically supplemented and co-coatomically semiperfect modules
Authors : Rafail Alizade, Serpil Güngör
Pages : 1417-1426
View : 11 | Download : 7
Publication Date : 2018-12-12
Article Type : Research
Abstract :In this paper it is shown that a factor module of an $\oplus$-co-coatomically supplemented module is not in general $\oplus$-co-coatomically supplemented. If $M$ is $\oplus$-co-coatomically supplemented and $U$ is a fully invariant submodule of $M$, then $M/U$ is $\oplus$-co-coatomically supplemented. A ring $R$ is left perfect if and only if $R^{(\mathbb{N})}$ is an $\oplus$-co-coatomically supplemented $R$-module. A projective module $M$ is co-coatomically semiperfect if and only if $M$ is $\oplus$-co-coatomically supplemented. A ring is semiperfect if and only if every finitely generated free $R$-module is co-coatomically semiperfect.Keywords : Co-coatomic submodule, $oplus$-co-coatomically supplemented module, co-coatomically semiperfect module