Commutative rings with toroidal zero-divisor graphs

Details Commutative rings with toroidal zero-divisor graphs Commutative rings with toroidal zero-divisor graphs

2007-02-15

arxiv.org/abs/math/0702451v4

Mathematics

Commutative Algebra

Revision and correction of Table 2. To appear in Houston Journal of Mathematics

Scientific paper

Let $R$ be a commutative ring and $\Gamma(R)$ denote its zero-divisor graph.
In this paper, we investigate the genus number of the compact Riemann surface
which $\Gamma(R)$ can be embedded and illustrate all finite commutative rings
$R$ (up to isomorphism) such that $\Gamma(R)$ is either toroidal or planar.

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