Results 111 to 120 of about 7,874 (214)

Zero-divisor graph of matrix rings and Hurwitz rings

, 2016
Let R be ring a with identity 1 ̸= 0, Sn(R) be a subring of the ring Tn(R) of n × n upper triangular matrices over R, and Hn(R) be the ring defined in the next section using HR, the ring of the Hurwitz series over R.
Abdioğlu, Cihat
core  

On zero-divisor graphs of infinite posets

Soft Computing
AbstractIt is known that the so-called Beck’s conjecture, i.e. the equality of the finite clique and chromatic numbers of a zero-divisor graph, holds for partially ordered sets Halaš and Jukl (Discrete Math 309(13):4584–4589, 2009). In this paper we present a simple direct proof of this fact.
Radomír Halas, Jozef Pócs
openaire   +1 more source

Strong zero-divisor graph of p.q.-Baer $*$-rings

In this paper, we study the strong zero-divisor graph of a p.q.-Baer $*$-ring. We determine the condition on a p.q.-Baer $*$-ring (in terms of the smallest central projection in a lattice of central projections of a $*$-ring), so that its strong zero ...
Waphare, B. N., Kumbhar, Nana, Khairnar, Anil   +2 more
core  

Graph Theoretic Properties of the Zero-Divisor Graph of a Ring

, 2004
Let R be a commutative ring with 1 ≠ 0, and let Z(R) denote the set of zero-divisors of R. One can associate with R a graph Γ(R) whose vertices are the nonzero zero-divisors of R.
Smith, Neal Oliver
core  

Zero-divisor semigroups and refinements of a star graph

, 2008
Let G be a refinement of a star graph with center c. Let Gc∗ be the subgraph of G induced on the vertex set V(G)∖{c or end vertices adjacent to c}. In this paper, we completely determine the structure of commutative zero-divisor semigroups S whose zero ...
Wu, Tongsuo, Liu, Qiong, Li Chen, Tongsuo Wu, Chen, Li, Qiong Liu   +5 more
core   +1 more source

The zero divisor graph of 2 x 2 matrices over a field

, 2016
A zero divisor graph, Γ(R), is formed from a ring R by having each element of Z(R)\{0} to be a vertex in the graph and having two vertices u and v adjacent if the corresponding elements from the ring are nonequal and have product equal to zero.
Ashrafi, Ali Reza, Tadayyonfar, Adel
core  

Generalizations of the Zero-Divisor Graph of a Ring

, 2001
Let R be a commutative ring with 1, and let Z(R) denote the set of zero­divisors of R. We define an undirected graph Γ(R) with vertices Z(R)* = Z(R) - {0}, where distinct vertices x and y of R are connected if and only if xy = 0. This graph is called the
Redmond, Shane Patrick
core  

Characterizations of Three Classes of Zero-Divisor Graphs

, 2012
The zero-divisor graph Γ(R) of a commutative ring R is the graph whose vertices consist of the nonzero zero-divisors of R such that distinct vertices x and y are adjacent if and only if xy = 0.
John D. LaGrange
core   +1 more source

Metric dimension of a zero-divisor graph

V diplomski nalogi preučujemo metrično dimenzijo grafa deliteljev niča kolobarja. Za kolobar $R$ definiramo njegov graf deliteljev niča $Gamma(R)$ kot enostaven neusmerjen graf, katerega vozlišča so delitelji niča, med dvema različnima vozliščema pa je ...
Možina, Tadeja
core  

Properties of ideal-based zero-divisor graphs of commutative rings

, 2014
Let R be a commutative ring with nonzero identity and I an ideal of R. The focus of this research is on a generalization of the zero-divisor graph called the ideal-based zero-divisor graph for commutative rings with nonzero identity.
Jesse Gerald Smith, Jr., Smith, Jesse Gerald, Jr.   +1 more
core