Commutative rings with toroidal zero-divisor graphs

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Let $R$ be a commutative ring and $Γ(R)$ denote its zero-divisor graph. In this paper, we investigate the genus number of the compact Riemann surface which $Γ(R)$ can be embedded and illustrate all finite commutative rings $R$ (up to isomorphism) such that $Γ(R)$ is either toroidal or planar.
Revision and correction of Table 2. To appear in Houston Journal of Mathematics

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Commutative Algebra, Combinatorics, 13A99; 05C10; 13M99

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http://salesiana.dossiersoluciones.com/handle/123456789/164972

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702451
 http://arxiv.org/abs/math/0702451

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arXiv