Results 41 to 50 of about 576,514 (220)
The total zero-divisor graph of commutative rings [PDF]
, 2018 In this paper we initiate the study of the total zero-divisor graphs over commutative rings with unity. These graphs are constructed by both relations that arise from the zero-divisor graph and from the total graph of a ring.
Đurić, Alen +3 more
core +2 more sources
Journal of Pure and Applied Algebra, 2008 Let \(R[x]\) be a polynomial ring over a ring \(R\). Then \(R\) is called a right McCoy (respectively left McCoy) ring if \(f(x)g(x)=0\) for each \(f(x),g(x)\neq 0\in R[x]\) implies that \((f(x))r=0\) for some \(r\neq 0\in R\) (respectively \(rg(x)=0\)), a McCoy ring is both left and right McCoy. The authors show some standard ring theoretic properties
Camillo, Victor, Nielsen, Pace P.
openaire +2 more sources
Component graphs of vector spaces and zero-divisor graphs of ordered sets
AKCE International Journal of Graphs and CombinatoricsIn this paper, nonzero component graphs and nonzero component union graphs of finite-dimensional vector spaces are studied using the zero-divisor graph of a specially constructed 0–1-distributive lattice and the zero-divisor graph of rings.
Nilesh Khandekar +2 more
doaj +1 more source
A note on the zero divisor graph of a lattice [PDF]
Transactions on Combinatorics, 2014 Let $L$ be a lattice with the least element $0$. An element $xin L$ is a zero divisor if $xwedge y=0$ for some $yin L^*=Lsetminus left{0right}$. The set of all zero divisors is denoted by $Z(L)$.
T. Tamizh Chelvam , S. Nithya
doaj
Distances in zero-divisor and total graphs from commutative rings–A survey
AKCE International Journal of Graphs and Combinatorics, 2016 There are so many ways to construct graphs from algebraic structures. Most popular constructions are Cayley graphs, commuting graphs and non-commuting graphs from finite groups and zero-divisor graphs and total graphs from commutative rings.
T. Tamizh Chelvam, T. Asir
doaj +1 more source
Boxicity of zero divisor graphs
Discrete Applied MathematicsA $d$-dimensional box is the cartesian product $R_i\times\cdots\times R_d$ where each $R_i$ is a closed interval on the real line. The boxicity of a graph, denoted as $box(G)$, is the minimum integer $d\geq 0$ such that $G$ is the intersection graph of a collection of $d$-dimensional boxes.
L. Sunil Chandran, Suraj Kumar Sahoo
openaire +2 more sources
GENERALIZATIONS OF THE ZERO-DIVISOR GRAPH
International Electronic Journal of Algebra, 2020 Summary: Let \(R\) be a commutative ring with \(1\neq 0\) and \(Z(R)\) its set of zerodivisors. The zero-divisor graph of \(R\) is the (simple) graph \(\Gamma \)(R) with vertices \(Z(R) \backslash \{0\}\), and distinct vertices \(x\)and \(y\) are adjacent if and only if \(xy= 0\).
ANDERSON, David F., MCCLURKİN, Grace
openaire +4 more sources
Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14
Mathematische Nachrichten, EarlyView.ABSTRACT The isometry between the type IV6 and the type II4 hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank 14 and of polarized abelian 8‐folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces
Flora Poon
wiley +1 more source
The n-zero-divisor graph of a commutative semigroup [PDF]
, 2022 Let S be a (multiplicative) commutative semigroup with 0, Z(S) the set of zero-divisors of S, and n a positive integer. The zero-divisor graph of S is the (simple) graph Γ(S) with vertices Z(S) ∗ = Z(S) \ {0}, and distinct vertices x and y are adjacent ...
Badawi, Ayman, Anderson, David F.
core +1 more source
Ring Classification of Ideal-Based Zero Divisor Graph with Vertices 9
Al-Kitab Journal for Pure SciencesLet R be a finite commutative ring with a non-zero unit, and L be an ideal of R. focuses on expanding the notation of the Zero Divisor Graph to create what is known as the Ideal-Based Zero Divisor Graph. The main goal is to classify rings using the ideal-
Husam Q. Mohammad +2 more
doaj +1 more source