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
- EP ID EP166026
- DOI -
- Views 30
- Downloads 0
Weak-hyperlattices derived from fuzzy congruences
In this paper we explore the connections between fuzzy congruence relations, fuzzy ideals and homomorphisms of hyperlattices. Indeed, we introduce the concept of fuzzy quotient set of hyperlattices as it was done in the...
ON Γ-SEMIRING WITH IDENTITY
In this paper we study the properties of structures of the semigroup (M, +) and the Γ-semigroup M of Γ-semiring M and regular Γ-semiring M satisfying the identity a + aαb = a or aαb + a = a or a + aαb + b = a or a + 1 =...
ZERO-DIVISOR GRAPHS OF REDUCED RICKART ∗-RINGS
For a ring A with an involution ∗, the zero-divisor graph of A, Γ∗ (A), is the graph whose vertices are the nonzero left zero-divisors in A such that distinct vertices x and y are adjacent if and only if xy∗ = 0. In this...
Jordan numbers, Stirling numbers and sums of powers
In the paper a new combinatorical interpretation of the Jordan numbers is presented. Binomial type formulae connecting both kinds of numbers mentioned in the title are given. The decomposition of the product of polynomia...
On balanced order relations and the normal hull of completely simple semirings
In [1] the authors proved that a semiring S is a completely simple semiring if and only if S is isomorphic to a Rees matrix semiring over a skew-ring R with sandwich matrix P and index sets I and Λ which are bands under...