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ON THE ANNIHILATOR GRAPH OF GROUP RINGS

2017
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Bulletin of the Korean Mathematical Society
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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 ∈ Z(R), let ann(a) = {r ∈ 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) = ann(x) ∪ ann(y). In this paper, we study the annihilator graph associated to a group ring RG.

doi:10.4134/bkms.b160135
fatcat:2pkl5z32f5ecxgxhxiyt6weaaa