The ideal-based zero-divisor graph of commutative chained rings

Abstract

Let I be a proper ideal of a commutative ring R with 1 = 0.The ideal-based zero-divisor graph of R with respect to I, denoted by ΓI (R), is the (simple) graph with vertices { x ∈ R \ I | xy ∈ I for some y ∈ R \ I }, and distinct vertices x and y are adjacent if and only if xy ∈ I.In this paper, we study ΓI (R) for commutative rings R such that R/I is a chained ring.