Commutative rings with toroidal zero-divisor graphs

By Hung-Jen Chiang-Hsieh, Neal O. Smith, Hsin-Ju Wang. 2007

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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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/eb1be81ae6f9e35ae974941a91772d67cd778de9