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

Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2014, Vol 34, Issue 1

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. 2010 Mathematics Subject Classification: 05C40, 05C45, 13A99

Authors and Affiliations

Z. Sarvandi, M. Kohan, S. Atani

Keywords

Related Articles

COMPLICATED BE-ALGEBRAS AND CHARACTERIZATIONS OF IDEALS

In this paper, using the notion of upper sets, we introduced the notions of complicated BE-Algebras and gave some related properties on complicated, self-distributive and commutative BE-algebras. In a self-distributive a...

IF-FILTERS OF PSEUDO-BL-ALGEBRAS

Characterizations of IF-filters of a pseudo-BL-algebra are established. Some related properties are investigated. The notation of prime IF- filters and a characterization of a pseudo-BL-chain are given. Homomorphisms of...

M-SOLID GENERALIZED NON-DETERMINISTIC VARIETIES

A generalized non-deterministic hypersubstitution is a mapping which maps operation symbols of type τ to the set of terms of the same type which does not necessarily preserve the arity. We apply the generalized nondeterm...

Generalized derivations in prime rings and Banach algebras

Let R be a prime ring with extended centroid C, F a generalized derivation of R and n ≥ 1, m ≥ 1 fixed integers. In this paper we study the situations: 1. (F(x ◦ y))m = (x ◦ y) n for all x, y ∈ I, where I is a nonzero id...

Filters of lattices with respect to a congruence

Some properties of filters on a lattice L are studied with respect to a congruence on L. The notion of a θ-filter of L is introduced and these filters are then characterized in terms of classes of θ. For distributive L,...

Download PDF file
  • EP ID EP166026
  • DOI -
  • Views 44
  • Downloads 0

How To Cite

Z. Sarvandi, M. Kohan, S. Atani (2014). An ideal-based zero-divisor graph of direct products of commutative rings. Discussiones Mathematicae - General Algebra and Applications, 34(1), -. https://europub.co.uk/articles/-A-166026