A generalization of the cozero-divisor graph of a commutative ring

چکیده مقاله

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 Γ_I(R), 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 Γ′(R) of R is the graph whose vertices are precisely the non-zero, non-unit elements of R and two distinct vertices x and y are adjacent if and only if x ∉ yR and y ∉ xR. In this paper, we introduced and investigated a new generalization of the cozero-divisor graph Γ′(R) of R denoted by Γ″_I(R). In fact, Γ″_I(R) is a dual notion of Γ_I(R). © 2025 World Scientific Publishing Company.