Commutative rings with toroidal zero-divisor graphs

• Autores: Hung-Jen Chiang-Hsieh, Neal O. Smith, Hsin-Ju Wang
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 36, Nº 1, 2010, págs. 1-31
• Idioma: inglés
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• Resumen

  • 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.