Ideal-Based Quasi Cozero Divisor Graph of a Commutative Ring

Faranak Farshadifar

Journal of Mathematics, 2025, vol. 2025, 1-7

Abstract: Let R be a commutative ring with identity and I be an ideal of R. The zero-divisor graph of R with respect to I, denoted by ΓIR, is the graph whose vertices are the set x∈R∖I xy∈I for some y∈R∖I with distinct vertices x and y are adjacent if and only if xy∈I. The cozero-divisor graph with respect to I, denoted by ΓI″R, is the graph of R with vertices x∈R∖IxR+I≠R and two distinct vertices x and y are adjacent if and only if x∉yR+I and y∉xR+I. In this paper, we introduced and investigated an undirected graph QΓI″R of R with vertices x∈R∖IxR+I≠R and xR+I=xR+I and two distinct vertices x and y are adjacent if and only if x∉yR+I and y∉xR+I.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4415087

DOI: 10.1155/jom/4415087

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