Commutative rings with toroidal zero-divisor graphs

Hung-Jen Chiang-Hsieh, Neal O. Smith, Hsin-Ju Wang

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 a…