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
- Mathematics(all)