The ideal-based zero-divisor graph of commutative chained rings
DOI:
https://doi.org/10.5644/SJM.10.1.01%20Keywords:
Zero-divisor graph, deal-based zero-divisor graph, chained ringAbstract
Let $I$ be a proper ideal of a commutative ring $R$ with $1 \neq 0$. The ideal-based zero-divisor graph of $R$ with respect to $I$, denoted by $\Gamma_I(R)$, is the (simple) graph with vertices $\{ \, x\in R \setminus I \mid xy \in I$ for some $y \in R\setminus I \, \}$, and distinct vertices $x$ and $y$ are adjacent if and only if $xy \in I$. In this paper, we study $\Gamma_I(R)$ for commutative rings $R$ such that $R/I$ is a chained ring.
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