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Communications in Algebra Volume 36, 2008 - Issue 2
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Original Articles

Classification of Rings with Genus One Zero-Divisor Graphs

Cameron Wickham Department of Mathematics, Missouri State University, Springfield, Missouri, USACorrespondence[email protected]
Pages 325-345 | Received 12 Oct 2006, Published online: 07 Apr 2008
 
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Abstract

This paper investigates properties of the zero-divisor graph of a commutative ring and its genus. In particular, we determine all isomorphism classes of finite commutative rings with identity whose zero-divisor graph has genus one.

2000 Mathematics Subject Classification:

ACKNOWLEDGMENT

The author wishes to thank the referee for a careful reading of this article and many useful comments.

Notes

Communicated by I. Swanson.

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