Zero-Divisor Graphs with respect to Ideals in Noncommutative Rings. (23rd October 2011)

• Record Type: Journal Article
• Authors: Ebrahimi Atani, Shahabaddin; Yousefian Darani, Ahmad
• Other Names: Klostermeyer W. F. Academic Editor.
• Is Part Of: ISRN discrete mathematics. Volume 2011(2011)
• Publication Date: 2011-10-23
• Subjects: Discrete mathematics -- Periodicals; Computer science -- Mathematics; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.5402/2011/459547
• Languages: English
• ISSNs: 2090-7788

Abstract

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.