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Amasya University, Faculty of Art and Science, Ipekkoy, Amasya, Turkey.
Abstract
We say that a module $M$ is a \emph{cms-module} if, for every cofinite submodule $N$ of $M$, there exist submodules $K$ and $K^{'}$ of $M$ such that $K$ is a supplement of $N$, and $K$, $K^{'}$ are mutual supplements in $M$. In this article, the various properties of cms-modules are given as a generalization of $\oplus$-cofinitely supplemented modules. In particular, we prove that a $\pi$-projective module $M$ is a cms-module if and only if $M$ is $\oplus$-cofinitely supplemented. Finally, we show that every free $R$-module is a cms-module if and only if $R$ is semiperfect.
Koşar, B., & Türkmen, B. N. (2016). A generalization of $\oplus$-cofinitely supplemented modules. Bulletin of the Iranian Mathematical Society, 42(1), 91-99.
MLA
B. Koşar; B. N. Türkmen. "A generalization of $\oplus$-cofinitely supplemented modules". Bulletin of the Iranian Mathematical Society, 42, 1, 2016, 91-99.
HARVARD
Koşar, B., Türkmen, B. N. (2016). 'A generalization of $\oplus$-cofinitely supplemented modules', Bulletin of the Iranian Mathematical Society, 42(1), pp. 91-99.
VANCOUVER
Koşar, B., Türkmen, B. N. A generalization of $\oplus$-cofinitely supplemented modules. Bulletin of the Iranian Mathematical Society, 2016; 42(1): 91-99.
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