An ideal-based zero-divisor graph of direct products of commutative rings

Shahabaddin Ebrahimi Atani; M. Shajari Kohan; Z. Ebrahimi Sarvandi

doi:10.7151/dmgaa.1211

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An ideal-based zero-divisor graph of direct products of commutative rings

Shahabaddin Ebrahimi Atani M. Shajari Kohan Z. Ebrahimi Sarvandi

Year: 2014 Journal: Discussiones Mathematicae - General Algebra and Applications Vol: 34 (1)Pages: 45-45 Publisher: De Gruyter Open

DOI: 10.7151/dmgaa.1211

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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 Mathematics Commutative ring Girth (graph theory) Primary ideal Category of rings Ideal (ethics) Graph Direct product Discrete mathematics Combinatorics Pure mathematics Commutative property Principal ideal ring

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Rings, Modules, and Algebras

Physical Sciences → Mathematics → Algebra and Number Theory

Commutative Algebra and Its Applications

Physical Sciences → Mathematics → Algebra and Number Theory

Advanced Topics in Algebra

Physical Sciences → Mathematics → Algebra and Number Theory

An ideal-based zero-divisor graph of direct products of commutative rings

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