English

Commutative rings with toroidal zero-divisor graphs

Commutative Algebra 2008-07-16 v4 Combinatorics

Abstract

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

Keywords

Cite

@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}
}

Comments

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