ArticleOriginal scientific text
Title
An ideal-based zero-divisor graph of direct products of commutative rings
Authors 1, 1, 1
Affiliations
- Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914 Rasht, Iran
Abstract
In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings.
Keywords
zero-divisor graph, ideal-based, diameter, girth, finite direct product
Bibliography
- D.F. Anderson and P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra. 217 (1999) 434-447. doi: 10.1006/jabr.1998.7840.
- M. Axtell, J. Stickles and J. Warfel, Zero-divisor graphs of direct products of commutative rings, Houston J. Math. 32 (2006) 985-994.
- D.F. Anderson, M.C. Axtell and J.A. Stickles Jr., Zero-divisor graphs in commutative rings in commutative Algebra-Noetherian and Non-Noetherian Perspectives (M. Fontana, S.E. Kabbaj, B. Olberding, I. Swanson, Eds), (Springer-Verlag, New York, 2011) 23-45. doi: 10.1007/978-1-4419-6990-3_2
- D.F. Anderson and A. Badawi, On the zero-divisor graph of a ring, Comm. Algebra 36 (2008) 3073-3092. doi: 10.1080/00927870802110888.
- I. Beck, Coloring of commutative rings, J. Algebra. 116 (1998) 208-226. doi: 10.1016/0021-8693(88)90202-5.
- S. Ebrahimi Atani and M. Shajari Kohan, On L-ideal-based L-zero-divisor graphs, Discuss. Math. Gen. Algebra Appl. 31 (2011) 127-145. doi: 10.7151/dmgaa.1178.
- S. Ebrahimi Atani and M. Shajari Kohan, L-zero-divisor graphs of direct products of L-commutative rings, Discuss. Math. Gen. Algebra Appl. 31 (2011) 159-174. doi: 10.7151/dmgaa.1180.
- S.P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra 31 (2003) 4425-4443. doi: 10.1081/AGB-120022801.
Pages:
45-53
Main language of publication
English
Received
2013-08-09
Accepted
2013-11-08
Published
2014
DOI: 10.7151/dmgaa.1211
Exact and natural sciences