Notes on the ideal-based zero-divisor graph

• Autorzy: Yousefian D.
• Języki publikacji: EN

Abstrakty

EN

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

EN

zero divisor; primal ideal

PL

dzielnik zera; ideał prymalny; teoria pierścieni

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2010
• Tom: Vol. 32
• Strony: 103--107
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Yousefian D.

• Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran,

Bibliografia

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• [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.