Commutative rings with toroidal zero-divisor graphs
Commutative Algebra
2008-07-16 v4 Combinatorics
Abstract
Let be a commutative ring and denote its zero-divisor graph. In this paper, we investigate the genus number of the compact Riemann surface which can be embedded and illustrate all finite commutative rings (up to isomorphism) such that is either toroidal or planar.
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