Commutative rings with toroidal zero-divisor graphs

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

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

Let R be a commutative ring and let Γ(R) denote its zero-divisor graph. We investigate the genus number of the compact Riemann surface in which Γ(R) can be embedded and explicitly determine all finite commutative rings R (up to isomorphism) such that Γ(R) is either toroidal or planar.

Original languageEnglish (US)
Pages (from-to)1-32
Number of pages32
JournalHouston Journal of Mathematics
Volume36
Issue number1
StatePublished - May 10 2010

Keywords

  • Planar
  • Toroidal
  • Zero-divisor graphs

ASJC Scopus subject areas

  • Mathematics(all)

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