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)|
|Number of pages||32|
|Journal||Houston Journal of Mathematics|
|State||Published - May 10 2010|
- Zero-divisor graphs
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