ISRN Discrete Mathematics
Volume 2011 (2011), Article ID 459547, 7 pages
Zero-Divisor Graphs with respect to Ideals in Noncommutative Rings
1Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran
2Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil 56199-11367, Iran
Received 15 July 2011; Accepted 25 August 2011
Academic Editor: W. F. Klostermeyer
Copyright © 2011 Shahabaddin Ebrahimi Atani and Ahmad Yousefian Darani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a commutative ring and an ideal of . The zero-divisor graph of with respect to , denoted (), is the undirected graph whose vertex set is for some with two distinct vertices and joined by an edge when . In this paper, we extend the definition of the ideal-based zero-divisor graph to noncommutative rings.