Rings whose associated extended zero-divisor graphs are complemented
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Let $R$ be a commutative ring with identity $1\neq 0$. In this paper, we continue the study started in \cite{DJF} to further investigate when the extended zero-divisor graph of $R$, denoted as $\overline{\Gamma}(R)$, is complemented. We also study when $\overline{\Gamma}(R)$ is uniquely complemented. We give a complete characterization of when $\overline{\Gamma}(R)$ of a finite ring $R$ is complemented. Various examples are given using the direct product of rings and idealizations of modules.
Abstract
Let $R$ be a commutative ring with identity $1\neq 0$. In this paper, we continue the study started in \cite{DJF} to further investigate when the extended zero-divisor graph of $R$, denoted as $\overline{\Gamma}(R)$, is complemented. We also study when $\overline{\Gamma}(R)$ is uniquely complemented. We give a complete characterization of when $\overline{\Gamma}(R)$ of a finite ring $R$ is complemented. Various examples are given using the direct product of rings and idealizations of modules.
참고문헌 (11)
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