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Chiang-Hsieh, Hung-Jen

Classification of rings with projective zero-divisor graphs. (English) Zbl 1143.13029

J. Algebra 319, No. 7, 2789-2802 (2008).
Let \(R\) be a commutative ring with identity, \(\Gamma(R)\) the zero-divisor graph of \(R.\) The paper investigates the embedding of \(\Gamma(R)\) into a non-orientable compact surface. If \(S\) is such a surface, \(S\) can be written as a of finite copies of projective planes. The number of these copies is called the crosscap number of \(S.\) A non- is called projective if it can be embedded into the projective plane. In the paper, the crosscap number of surfaces in which \(\Gamma(R)\) can be embedded is investigated, as well as all finite rings with projective zero-divisor graphs.
Reviewer: Christodor-Paul Ionescu (Bucureşti)

Cited in 1 Review
Cited in 31 Documents

MSC:

13M05 Structure of finite commutative rings
05C99 Graph theory

Keywords:

projective zero-divisor graph; crosscap number
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Full Text: DOI

References:

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