Commutative rings with toroidal zero-divisor graphs

Abstract

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.

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

Cited by in corpus (1)

• Genera of zero-divisor graphs with respect to ideals