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Valuation Rings with Zero Divisors [PDF]
Proceedings of the American Mathematical Society, 1971 Manis has developed a valuation theory for commutative rings which extends valuation theory for fields. However his results do not extend the characterization of valuation rings as domains of maximal partial homomorphisms. In this note we show that Manis’ theory also generalizes this aspect of valuation theory.
Max D. Larsen, Patrick H. Kelly
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Zero-divisors of Semigroup Modules
Kyungpook mathematical journal, 2011 Let $M$ be an $R$-module and $S$ a semigroup. Our goal is to discuss zero-divisors of the semigroup module $M[S]$. Particularly we show that if $M$ is an $R$-module and $S$ a commutative, cancellative and torsion-free monoid, then the $R[S]$-module $M[S]$ has few zero-divisors of degree $n$ if and only if the $R$-module $M$ has few zero-divisors of ...
Peyman Nasehpour
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Non Deterministic Zero Divisor Graph
Ratio Mathematica, 2023 A non-deterministic zero divisor graph refers to an element in a ring or algebraic structure that can multiply with another element to give zero, but the specific outcome of the multiplication is not uniquely determined.
Shakila Banu, Naveena Selvaraj
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Distributive lattices and some related topologies in comparison with zero-divisor graphs [PDF]
Categories and General Algebraic Structures with Applications, 2021 In this paper,for a distributive lattice $\mathcal L$, we study and compare some lattice theoretic features of $\mathcal L$ and topological properties of the Stone spaces ${\rm Spec}(\mathcal L)$ and ${\rm Max}(\mathcal L)$ with the corresponding graph ...
Saeid Bagheri, mahtab Koohi Kerahroodi
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SP-rings with zero-divisors [PDF]
Communications in Algebra, 2016 We characterize the commutative rings whose ideals (resp. regular ideals) are products of radical ideals.
Malik Tusif Ahmed, Tiberiu Dumitrescu
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ON THE ANALYTIC ZERO DIVISOR CONJECTURE OF LINNELL [PDF]
Bulletin of the London Mathematical Society, 2003 In this note we prove that in the case of finitely generated amenable groups the classical zero divisor conjecture implies the analytic zero divisor conjecture of Linnell.
Gábor Elek
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Upper dimension and bases of zero-divisor graphs of commutative rings
AKCE International Journal of Graphs and Combinatorics, 2020 For a commutative ring with non-zero zero divisor set , the zero divisor graph of is with vertex set , where two distinct vertices and are adjacent if and only if .
S. Pirzada, M. Aijaz, S.P. Redmond
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On the eigenvalues of zero-divisor graph associated to finite commutative ring
AKCE International Journal of Graphs and Combinatorics, 2021 Let Z(R) be the set of zero-divisors of a commutative ring R with non-zero identity and be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by is a simple graph whose vertex set is and two vertices are adjacent if and only if ...
S. Pirzada +2 more
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McCoy rings and zero-divisors [PDF]
Journal of Pure and Applied Algebra, 2008 AbstractWe investigate relations between the McCoy property and other standard ring theoretic properties. For example, we prove that the McCoy property does not pass to power series rings. We also classify how the McCoy property behaves under direct products and direct sums.
Pace P. Nielsen, Victor Camillo
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On graphs with equal coprime index and clique number
AKCE International Journal of Graphs and Combinatorics, 2023 Recently, Katre et al. introduced the concept of the coprime index of a graph. They asked to characterize the graphs for which the coprime index is the same as the clique number. In this paper, we partially solve this problem.
Chetan Patil +2 more
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