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Sub-semigroups determined by the zero-divisor graph

Discrete Mathematics, 2008
In this paper we study sub-semigroups of a finite or an infinite zero-divisor semigroup S determined by properties of the zero-divisor graph Γ(S). We use these sub-semigroups to study the correspondence between zero-divisor semigroups and zero-divisor ...
Tongsuo Wu, Dancheng Lu
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The Zero-Divisor Graph of a Lattice

Results in Mathematics, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Estaji, E., Khashyarmanesh, K.
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Classification of Rings with Genus One Zero-Divisor Graphs

Communications in Algebra, 2008
. This paper investigates properties of the zero-divisor graph of a commutative ring and its genus. In particular, we determine all isomorphism classes of finite commutative rings with identity whose zero-divisor graph has genus 1 ...
Cameron Wickham
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On zero-divisor graphs of finite rings

Journal of Algebra, 2007
The zero-divisor graph of a ring R is defined as the directed graph Γ(R) that its vertices are all non-zero zero-divisors of R in which for any two distinct vertices x and y, x→y is an edge if and only if xy=0.
S Akbari
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Zero Divisors of Atomic Functions

The Annals of Mathematics, 1992
The authors develop a theory of zero divisors or zero currents for sections of a vector bundle under an orientation condition. An \(R^ n\)- valued function is said to be atomic if the function pulls back the basic forms \(dy^ I/| y|^ p\) on \(R^ n\) to locally Lebesgue integrable forms on the domain manifold in the range \(p=| I| \leq n-1\).
Harvey, F. Reese, Semmes, Stephen W.
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The k-zero-divisor hypergraph

Ricerche di Matematica, 2011
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Haouaoui, Amor, Benhissi, Ali
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NORMAL PAIRS WITH ZERO-DIVISORS

Journal of Algebra and Its Applications, 2011
Results of Davis on normal pairs (R, T) of domains are generalized to (commutative) rings with nontrivial zero-divisors, particularly complemented rings. For instance, if T is a ring extension of an almost quasilocal complemented ring R, then (R, T) is a normal pair if and only if there is a prime ideal P of R such that T = R[P], R/P is a valuation ...
Dobbs, David E., Shapiro, Jay
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Zero-divisors and zero-divisor graphs of power series rings

Ricerche di Matematica, 2015
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Haouaoui, Amor, Benhissi, Ali
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Zero divisors in quaternion algebras

Journal of Algorithms, 1988
The starting point for the author is the following pair of problems: Given an associative algebra A, can we decide whether or not there are zero divisors and if so, can we outline an algorithm to construct a pair of zero divisors; in particular, in what time can it be done?
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The rings where zero-divisor polynomials have zero-divisor coefficients

Rocky Mountain Journal of Mathematics, 2021
The aim of this paper is to introduce and study a new class of rings which is called \(\mathrm{ZPZC}\) rings. It is shown that every right McCoy ring is a \(\mathrm{ZPZC}\) ring, and an example is given to show that a \(\mathrm{ZPZC}\) ring need not be right McCoy.
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