Commutative rings with toroidal zero-divisor graphs

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

Research output: Contribution to journalArticle

29 Citations (Scopus)

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

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Zero-divisor Graph
Commutative Ring
Finite Rings
Riemann Surface
Isomorphism
Genus
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Keywords

  • Planar
  • Toroidal
  • Zero-divisor graphs

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Commutative rings with toroidal zero-divisor graphs. / Chiang-Hsieh, Hung Jen; Smith, Neal O; Wang, Hsin J.U.

In: Houston Journal of Mathematics, Vol. 36, No. 1, 10.05.2010, p. 1-32.

Research output: Contribution to journalArticle

Chiang-Hsieh, HJ, Smith, NO & Wang, HJU 2010, 'Commutative rings with toroidal zero-divisor graphs', Houston Journal of Mathematics, vol. 36, no. 1, pp. 1-32.
Chiang-Hsieh, Hung Jen ; Smith, Neal O ; Wang, Hsin J.U. / Commutative rings with toroidal zero-divisor graphs. In: Houston Journal of Mathematics. 2010 ; Vol. 36, No. 1. pp. 1-32.
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