Commutative rings with toroidal zero-divisor graphs

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

Commutative rings with toroidal zero-divisor graphs

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

Mathematics

Research output: Contribution to journal › Article › peer-review

50 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 language	English (US)
Pages (from-to)	1-32
Number of pages	32
Journal	Houston Journal of Mathematics
Volume	36
Issue number	1
State	Published - 2010

Keywords

Planar
Toroidal
Zero-divisor graphs

ASJC Scopus subject areas

General Mathematics

Cite this

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title = "Commutative rings with toroidal zero-divisor graphs",

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.",

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author = "Chiang-Hsieh, {Hung Jen} and Smith, {Neal O.} and Wang, {Hsin J.U.}",

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journal = "Houston Journal of Mathematics",

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publisher = "University of Houston",

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T1 - Commutative rings with toroidal zero-divisor graphs

AU - Chiang-Hsieh, Hung Jen

AU - Smith, Neal O.

AU - Wang, Hsin J.U.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Planar

KW - Toroidal

KW - Zero-divisor graphs

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UR - http://www.scopus.com/inward/citedby.url?scp=77951870374&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77951870374

SN - 0362-1588

VL - 36

SP - 1

EP - 32

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

IS - 1

ER -

Commutative rings with toroidal zero-divisor graphs

Abstract

Keywords

ASJC Scopus subject areas

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