ON THE ANNIHILATOR GRAPH OF GROUP RINGS

被引：1

作者：

Afkhami, Mojgan ^{[1
]}

Khashyarmanesh, Kazem ^{[2
]}

Salehifar, Sepideh ^{[2
]}

机构：

[1] Univ Neyshabur, Dept Math, POB 91136-899, Neyshabur, Iran

[2] Ferdowsi Univ Mashhad, Dept Pure Math, POB 1159-91775, Mashhad, Iran

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2017年 / 54卷 / 01期

关键词：

zero-divisor graph; annihilator graph; bipartite graph; planar graph; line graph; ZERO-DIVISOR GRAPHS; COMMUTATIVE RING;

D O I：

10.4134/BKMS.b160135

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a commutative ring with nonzero identity and G be a nontrivial finite group. Also, let Z(R) be the set of zero-divisors of R and, for a epsilon Z(R), let ann(a) = {r epsilon R | ra = 0}. The annihilator graph of the group ring RG is defined as the graph AG(RG), whose vertex set consists of the set of nonzero zero-divisors, and two distinct vertices x and y are adjacent if and only if ann(xy) not equal ann(x) boolean OR ann(y). In this paper, we study the annihilator graph associated to a group ring RG.

引用

页码：331 / 342

页数：12