Results 181 to 190 of about 576,514 (220)
On Domination in Zero-Divisor Graphs [PDF]
Canadian Mathematical Bulletin, 2013 AbstractWe first determine the domination number for the zero-divisor graph of the product of two commutative rings with 1. We then calculate the domination number for the zero-divisor graph of any commutative artinian ring. Finally, we extend some of the results to non-commutative rings in which an element is a left zero-divisor if and only if it is a
Rad, Nader Jafari +2 more
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k-Zero-Divisor and Ideal-Based k-Zero-Divisor Hypergraphs of Some Commutative Rings [PDF]
Symmetry, 2021 Let R be a commutative ring with nonzero identity and k≥2 be a fixed integer. The k-zero-divisor hypergraph Hk(R) of R consists of the vertex set Z(R,k), the set of all k-zero-divisors of R, and the hyperedges of the form {a1,a2,a3,…,ak}, where a1,a2,a3,…
Ratinan Boonklurb, Boonklurb Ratinan
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Sub-semigroups determined by the zero-divisor graph [PDF]
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 ...
Dancheng Lu, Tongsuo Wu
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Zero Divisors and Orlicz Spaces
Journal of Mathematical Sciences, 2022Let \(G\) be a countable discrete group and let \(\Phi\) be a Young function on \(G\). Let \(\alpha\) be a nonzero element in \(\ell^1(G)\) and denote convolution of functions on \(G\) by \(\ast\). We shall say that \(\alpha\) is a \(\Phi\)-zero divisor if there exists a nonzero function \(\beta\) in the Orlicz space \(\ell^{\Phi}(G)\) that satisfies \(
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The Zero-Divisor Graph of a Lattice
Results in Mathematics, 2010zbMATH 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 [PDF]
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 [PDF]
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.
Saieed Akbari
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NORMAL PAIRS WITH ZERO-DIVISORS
Journal of Algebra and Its Applications, 2011Results 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, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haouaoui, Amor, Benhissi, Ali
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Zero Divisors of Atomic Functions
The Annals of Mathematics, 1992The 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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