Results 11 to 20 of about 88,527 (242)
The wiener index of the zero-divisor graph for a new class of residue class rings [PDF]
Frontiers in Chemistry, 2022 The zero-divisor graph of a commutative ring R, denoted by Γ(R), is a graph whose two distinct vertices x and y are joined by an edge if and only if xy = 0 or yx = 0.
Yinhu Wei, Ricai Luo
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Smarandache Zero Divisors [PDF]
, 2001 Studying the notion of Smarandache zero divisor in semigroups and rings, illustrating them with examples and proving some interesting results about them.
Vasantha, Kandasamy
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A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs [PDF]
HeliyonThis article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if ...
Nasir Ali +4 more
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Zero Divisors and Orlicz Spaces [PDF]
Journal of Mathematical Sciences, 2022 Let \(G\) 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 \(
Yaroslav Kopylov
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Resolving Zero Divisors Using Hensel Lifting [PDF]
2017 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2017 Algorithms which compute modulo triangular sets must respect the presence of zero-divisors. We present Hensel lifting as a tool for dealing with them. We give an application: a modular algorithm for computing GCDs of univariate polynomials with coefficients modulo a radical triangular set over the rationals.
John Kluesner, Michael Monagan
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On irreducible divisor graphs in commutative rings with zero-divisors
International Electronic Journal of Algebra, 2015 In this paper, we continue the program initiated by I. Beck's now classical paper concerning zero-divisor graphs of commutative rings. After the success of much research regarding zero-divisor graphs, many authors have turned their attention to studying divisor graphs of non-zero elements in integral domains.
Christopher Park Mooney
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The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring
Contemporary Mathematics and Applications (ConMathA)The zero-divisor graph of a commutative ring is a graph where the vertices represent the zero-divisors of the ring, and two distinct vertices are connected if their product equals zero.
Jinan Ambar +2 more
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Fault-Tolerant Edge Metric Dimension of Zero-Divisor Graphs of Commutative Rings [PDF]
AxiomsIn recent years, the intersection of algebraic structures and graph-theoretic concepts has developed significant interest, particularly through the study of zero-divisor graphs derived from commutative rings.
Omaima Alshanquiti +2 more
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Zero-divisor graphs and zero-divisor functors
Journal of Algebra and Its Applications, 2023 Inspired by a very recent work of A. Đurić, S. Jevđenić and N. Stopar, we introduce a new definition of zero-divisor graphs attached to rings that includes all of the classical definitions already known in the literature. We provide an interpretation of such graphs by means of a functor that we call zero-divisor functor and which is associated with a ...
Enrico Sbarra, Maurizio Zanardo
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Classification of Zero Divisor Graphs of Commutative Rings of Degrees 11,12 and 13 [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2014 In 2005 Wang investigated the zero divisor graphs of degrees 5,6,9 and 10. In 2012 Shuker and Mohammad investigated the zero divisor graphs of degrees 7 and 8. In this paper, we consider zero divisor graphs of commutative rings of degrees 11, 12 and 13.
Nazar Shuker, Husam Mohammad
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