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http://dx.doi.org/10.4134/BKMS.b160135

ON THE ANNIHILATOR GRAPH OF GROUP RINGS  

Afkhami, Mojgan (Department of Mathematics University of Neyshabur)
Khashyarmanesh, Kazem (Department of Pure Mathematics Ferdowsi University of Mashhad)
Salehifar, Sepideh (Department of Pure Mathematics Ferdowsi University of Mashhad)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.1, 2017 , pp. 331-342 More about this Journal
Abstract
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 $a{\in}Z(R)$, let $ann(a)=\{r{\in}R{\mid}ra=0\}$. 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 $ann(xy){\neq}ann(x){\cup}ann(y)$. In this paper, we study the annihilator graph associated to a group ring RG.
Keywords
zero-divisor graph; annihilator graph; bipartite graph; planar graph; line graph;
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