We also investigate the interplay between the ring theoretic properties of a Noetherian multiplication ring $R$ and the graph-theoretic properties of $Q\Gamma_{I}(R)$.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $R$ be a commutative ring with identity and $I$ a proper ideal of $R$.
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Key Findings & Data:In this paper we introduce the ideal-based quasi zero divisor graph $Q\Gamma_{I}(R)$ of $R$ with respect to $I$ which is an undirected graph with vertex set $V=\{a\in R\backslash\sqrt{I}:$ $ab\in I$ for some $b\in R\backslash\sqrt{I}\}$ and two distinct vertices $a$ and $b$ are adjacent if and only if $ab\in I$.
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Conclusion & Impact:We also investigate the interplay between the ring theoretic properties of a Noetherian multiplication ring $R$ and the graph-theoretic properties of $Q\Gamma_{I}(R)$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ideal-based zero divisor graph · quasi primary ideal · zero-divisor graph
Abstract
Let $R$ be a commutative ring with identity and $I$ a proper ideal of $R$. In this paper we introduce the ideal-based quasi zero divisor graph $Q\Gamma_{I}(R)$ of $R$ with respect to $I$ which is an undirected graph with vertex set $V=\{a\in R\backslash\sqrt{I}:$ $ab\in I$ for some $b\in R\backslash\sqrt{I}\}$ and two distinct vertices $a$ and $b$ are adjacent if and only if $ab\in I$. We study the basic properties of this graph such as diameter, girth, dominaton number, etc. We also investigate the interplay between the ring theoretic properties of a Noetherian multiplication ring $R$ and the graph-theoretic properties of $Q\Gamma_{I}(R)$.
Çelikel, E. Y., Das, A., Abdioğlu, C. (2022). Ideal-based quasi zero divisor graph. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 6, 1658–1666. https://ajindex.com/articles/529460
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