Results 101 to 110 of about 88,501 (223)
The k-Zero-Divisor Hypergraph of a Commutative Ring
International Journal of Mathematics and Mathematical Sciences, 2007 The concept of the zero-divisor graph of a commutative ring has been studied by many authors, and the k-zero-divisor hypergraph of a commutative ring is a nice abstraction of this concept.
Ch. Eslahchi, A. M. Rahimi
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Compressed zero-divisor graphs of noncommutative rings
, 2018 We extend the notion of the compressed zero-divisor graph $\varTheta(R)$ to noncommutative rings in a way that still induces a product preserving functor $\varTheta$ from the category of finite unital rings to the category of directed graphs.
Jevđenić, Sara +2 more
core
The 2‐divisibility of divisors on K3 surfaces in characteristic 2
Mathematische Nachrichten, Volume 298, Issue 6, Page 1964-1988, June 2025.Abstract We show that K3 surfaces in characteristic 2 can admit sets of n$n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each n=8,12,16,20$n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only n=
Toshiyuki Katsura +2 more
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The diameter of a zero divisor graph
Journal of Algebra, 2006 AbstractLet R be a commutative ring and let Z(R)∗ be its set of nonzero zero divisors. The set Z(R)∗ makes up the vertices of the corresponding zero divisor graph, Γ(R), with two distinct vertices forming an edge if the product of the two elements is zero.
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τ-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.
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On the genus of graphs from commutative rings
AKCE International Journal of Graphs and Combinatorics, 2017 Let be a commutative ring with non-zero identity. The cozero-divisor graph of , denoted by , is a graph with vertex-set , which is the set of all non-zero non-unit elements of , and two distinct vertices and in are adjacent if and only if and , where for
S. Kavitha, R. Kala
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Rings in which every left zero-divisor is also a right zero-divisor and conversely
Journal of Algebra and Its Applications, 2019 A ring [Formula: see text] is called eversible if every left zero-divisor in [Formula: see text] is also a right zero-divisor and conversely. This class of rings is a natural generalization of reversible rings. It is shown that every eversible ring is directly finite, and a von Neumann regular ring is directly finite if and only if it is eversible. We
Ghashghaei, E. +3 more
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Independent sets of some graphs associated to commutative rings
, 2013 Let $G=(V,E)$ be a simple graph. A set $S\subseteq V$ is independent set of $G$, if no two vertices of $S$ are adjacent. The independence number $\alpha(G)$ is the size of a maximum independent set in the graph.
Communicated A. R. Ashrafi +2 more
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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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On generalized topological divisors of zero in real m-convex algebras [PDF]
, 1967 W. Żelazko
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