Results 161 to 170 of about 24,531 (183)
Some of the next articles are maybe not open access.
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
openaire +2 more sources
Signed Zero-Divisor Graphs Over Commutative Rings
Communications in Mathematics and Statistics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lu Lu, Lihua Feng, Weijun Liu
openaire +2 more sources
Properties of Zero-divisor Graphs
2021In this chapter, we deal with some graph-theoretical properties of the zero-divisor graph of a commutative ring such as colorings, connectedness, bipartite nature, isomorphisms, and automorphisms.
David F. Anderson +3 more
openaire +1 more source
Zero-divisor Labelings of Graphs
Communications in Algebra, 2016This paper introduces the notions of a zero-divisor labeling and the zero-divisor index of a graph using the zero-divisors of a commutative ring. Viewed in this way, the usual zero-divisor graph is a maximal graph with respect to a zero-divisor labeling. We also study optimal zero-divisor labelings of a finite graph.
null Pranjali +3 more
openaire +1 more source
Zero-divisor graphs of amalgamations
MATHEMATICA SCANDINAVICA, 2018Let $f\colon A\rightarrow B$ be a homomorphism of commutative rings and let $J$ be an ideal of $B$. The amalgamation of $A$ with $B$ along $J$ with respect to $f$ is the subring of $A\times B$ given by \[ A\bowtie ^{f}J:=\{(a,f(a)+j) \mid a\in A, j\in J\}. \] This paper investigates the zero-divisor graph of amalgamations.
Salah-Eddine Kabbaj, Abdeslam Mimouni
openaire +1 more source
2021
In this chapter, we study topological concepts like the genus of zero-divisor graphs. The prime objective of topological graph theory is to draw a graph on a surface so that no two edges cross, an intuitive geometric problem that can be enriched by specifying symmetries or combinatorial side-conditions.
David F. Anderson +3 more
openaire +1 more source
In this chapter, we study topological concepts like the genus of zero-divisor graphs. The prime objective of topological graph theory is to draw a graph on a surface so that no two edges cross, an intuitive geometric problem that can be enriched by specifying symmetries or combinatorial side-conditions.
David F. Anderson +3 more
openaire +1 more source
Distances in Zero-divisor Graphs
2021These concepts are the considerations of this chapter. Actually, we present results concerning the diameter, girth, and center of the zero-divisor graph of a commutative ring. We begin the chapter by introducing and discussing some basic concepts of the zero-divisor graph of a commutative ring.
David F. Anderson +3 more
openaire +1 more source
RECOVERING RINGS FROM ZERO-DIVISOR GRAPHS
Journal of Algebra and Its Applications, 2013Suppose G is the zero-divisor graph of some commutative ring with 1. When G has four or more vertices, a method is presented to find a specific commutative ring R with 1 such that Γ(R) ≅ G. Furthermore, this ring R can be written as R ≅ R1 × R2 × ⋯ × Rn, where each Ri is local and this representation of R is unique up to factors Ri with isomorphic ...
openaire +2 more sources
On Realizing Zero-Divisor Graphs
Communications in Algebra, 2008An algorithm is presented for constructing the zero-divisor graph of a direct product of integral domains. Moreover, graphs which are realizable as zero-divisor graphs of direct products of integral domains are classified, as well as those of Boolean rings.
openaire +1 more source
A Characterization of Bipartite Zero-divisor Graphs
Canadian Mathematical Bulletin, 2014AbstractIn this paper we obtain a characterization for all bipartite zero-divisor graphs of commutative rings R with 1 such that R is finite or |Nil(R)| ≠ 2.
Rad, Nader Jafari, Jafari, Sayyed Heidar
openaire +1 more source