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

Authors : Rafail ALİZADE, Serpil GÜNGÖR

Pages : 1417-1426

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Publication Date : 2018-12-12

Article Type : Research Paper

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 $R^{insert ignore into journalissuearticles values(\mathbb{N});}$ 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