Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Let I be an ideal of a commutative ring R. Denote by S(I) the set {x ∈ R | xy ∈ I for some y ∈ R \ I}. The zero-divisor graph of R with respect to I is an undirected graph, denoted by [wzór], with vertices S(I) \ I where distinct vertices x and y are adjacent if and only if xy ∈ I. In this paper we study the diameter and the girth of [wzór], when the prime ideals of R contained in S(I) are linearly ordered.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
103--107
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
- Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran, yousefian@uma.ac.ir
Bibliografia
- [1] D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), 434-447.
- [2] A. Badawi On domains which have prime ideals that are linearly ordered, Comm. Algebra, 23 (1995), 4365-4373.
- [3] I. Beck, Coloring of commutative rings. J. Algebra, 116 (1988), 208-226.
- [4] S. Ebrahimi Atani and A. Youse_an Darani, Zero-divisor graph with respect to primal and weakly primal ideals, J. Korean Math. Soc. 46 (2)(2009)
- [5] L. Fuchs, On primal ideals, Proc. Amer. Math. Soc. 1 (1950), 1-6.
- [6] T. G. Lucas, The diameter of a zero-divisor graph, J. Algebra 301 (2006), 174-193.
- [7] H. R. Maimani, M. R. Pournaki and S. Yassemi, Zero-divisor graph with respect to an ideal, Comm. Algebra 34 (2006), 923-929.
- [8] S. B. Mulay, Rings having zero-divisor graphs of small diameter or large girth, Bull. Ausstral. Math. Soc., 72 (2005), 481-490.
- [9] S. P. Redmond, An ideal-based zero-divisor graph of a commutative ring, Comm. Algebra 31 (2003), 4425-4443.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA7-0039-0023