Resumen de Commutative rings with toroidal zero-divisor graphs

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

• We investigate the genus number of compact Riemann surface in which the zero-divisor graphs of commutative rings can be embedded and explicitly determine all finite commutative rings (up to isomorphism) such that their zero-divisor graphs are either planar or toroidal.