L-zero-divisor graphs of direct products of L-commutative rings

S. Ebrahimi Atani; M. Shajari Kohan

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Displaying similar documents to “L-zero-divisor graphs of direct products of L-commutative rings”

A class of zero divisor rings in which every graph is precisely the union of a complete graph and a complete bipartite graph

Syed Khalid Nauman, Basmah H. Shafee (2015)

Open Mathematics

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Recently, an interest is developed in estimating genus of the zero-divisor graph of a ring. In this note we investigate genera of graphs of a class of zero-divisor rings (a ring in which every element is a zero divisor). We call a ring R to be right absorbing if for a; b in R, ab is not 0, then ab D a. We first show that right absorbing rings are generalized right Klein 4-rings of characteristic two and that these are non-commutative zero-divisor local rings. The zero-divisor graph of...

A variation of zero-divisor graphs

Raibatak Sen Gupta, M.K. Sen, Shamik Ghosh (2015)

Discussiones Mathematicae - General Algebra and Applications

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

S. Ebrahimi Atani, M. Shajari Kohan, Z. Ebrahimi Sarvandi (2014)

Discussiones Mathematicae - General Algebra and Applications

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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.

Real closures of commutative rings. II.

Manfred Knebusch (1976)

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On graphs associated to rings.

Petrović, Zoran Z., Moconja, Slavko M. (2008)

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Some small-centralizer properties for rings.

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Some properties of the zero divisor graph of a commutative ring

Khalida Nazzal, Manal Ghanem (2014)

Discussiones Mathematicae - General Algebra and Applications

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Let Γ(R) be the zero divisor graph for a commutative ring with identity. The k-domination number and the 2-packing number of Γ(R), where R is an Artinian ring, are computed. k-dominating sets and 2-packing sets for the zero divisor graph of the ring of Gaussian integers modulo n, Γ(ℤₙ[i]), are constructed. The center, the median, the core, as well as the automorphism group of Γ(ℤₙ[i]) are determined. Perfect zero divisor graphs Γ(R) are investigated.

An addendum to the paper: “Arithmetic functions over rings with zero divisors” by Ruangsinsap, Laohakosol and P. Udomkavanich.

Narkiewicz, Władysław, Ruengsinsub, Pattira, Laohakosol, Vichian (2004)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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On the intersection graphs of ideals of direct product of rings

Nader Jafari Rad, Sayyed Heidar Jafari, Shamik Ghosh (2014)

Discussiones Mathematicae - General Algebra and Applications

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In this paper we first calculate the number of vertices and edges of the intersection graph of ideals of direct product of rings and fields. Then we study Eulerianity and Hamiltonicity in the intersection graph of ideals of direct product of commutative rings.

On rings with alternators in the commutative center

Kleinfeld, Erwin (1993)

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Rings of type $(γ, δ)$ without zero divisors are associative

Kleinfeld, Erwin, Kleinfeld, Margaret Humm (1977)

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Characterizing which Powers of Hypercubes and Folded Hyper- cubes Are Divisor Graphs

Eman A. AbuHijleh, Omar A. AbuGhneim, Hasan Al-Ezeh (2015)

Discussiones Mathematicae Graph Theory

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In this paper, we show that Qkn is a divisor graph, for n = 2, 3. For n ≥ 4, we show that Qkn is a divisor graph iff k ≥ n − 1. For folded-hypercube, we get FQn is a divisor graph when n is odd. But, if n ≥ 4 is even integer, then FQn is not a divisor graph. For n ≥ 5, we show that (FQn)k is not a divisor graph, where 2 ≤ k ≤ [n/2] − 1.

On the Radius and the Relation Between the Total Graph of a Commutative Ring and Its Extensions

Zoran Pucanović, Zoran Petrović (2011)

Publications de l'Institut Mathématique

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