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arXiv · 1701.06398

When the Annihilator Graph of a Commutative Ring Is Planar or Toroidal?

Mohammad Javad Nikmehr·Reza Nikandish·Moharam Bakhtyiari
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Abstract

Let $R$ be a commutative ring with identity, and let $Z(R)$ be the set of zero-divisors of $R$. The annihilator graph of $R$ is defined as the undirected graph $AG(R)$ with the vertex set $Z(R)^*=Z(R)\setminus\{0\}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $ann_R(xy)\neq ann_R(x)\cup ann_R(y)$. In this paper, all rings whose annihilator graphs can be embed on the plane or torus are classified.

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Mohammad Javad Nikmehr, Reza Nikandish, Moharam Bakhtyiari. 2017-01-27. When the Annihilator Graph of a Commutative Ring Is Planar or Toroidal?. https://arxiv.org/abs/1701.06398

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