Commutative rings with toroidal zero-divisor graphs

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

Commutative rings with toroidal zero-divisor graphs

交换代数 2008-07-16 v4 组合数学

作者: Hung-Jen Chiang-Hsieh , Neal O. Smith , Hsin-Ju Wang

摘要

Let $R$ be a commutative ring and $\Gamma(R)$ denote its zero-divisor graph. In this paper, we investigate the genus number of the compact Riemann surface which $\Gamma(R)$ can be embedded and illustrate all finite commutative rings $R$ (up to isomorphism) such that $\Gamma(R)$ is either toroidal or planar.

关键词

zero-divisor graphs commutative ring theory mapping class groups of surfaces

引用

@article{arxiv.math/0702451,
  title  = {Commutative rings with toroidal zero-divisor graphs},
  author = {Hung-Jen Chiang-Hsieh and Neal O. Smith and Hsin-Ju Wang},
  journal= {arXiv preprint arXiv:math/0702451},
  year   = {2008}
}

备注

Revision and correction of Table 2. To appear in Houston Journal of Mathematics

Commutative rings with toroidal zero-divisor graphs

摘要

关键词

引用

备注

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