$\oplus$-co-coatomically supplemented and co-coatomically semiperfect modules

Year 2018, Volume: 47 Issue: 6, 1417 - 1426, 12.12.2018

Rafail Alizade , Serpil Güngör

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

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