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
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
收藏
页码:331 / 342
页数:12
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