Zero-Divisor Graphs with respect to Ideals in Noncommutative Rings. (23rd October 2011) - Ebrahimi Atani, Shahabaddin; Yousefian Darani, Ahmad
Abstract : LetR be a commutative ring andI an ideal ofR . The zero-divisor graph ofR with respect toI, denotedΓ I (R ), is the undirected graph whose vertex set is{ x ∈ R ∖ I | x y ∈ I for somey ∈ R ∖ I } with two distinct verticesx andy joined by an edge whenx y ∈ I . In this paper, we extend the definition of the ideal-based zero-divisor graph to noncommutative rings.