Classification of rings with projective zero-divisor graphs
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 connected sum of finite copies of projective planes. The number of these copies is called the crosscap number of \(S.\) A non-planar graph 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.
scientific article; zbMATH DE number 5277613
scientific article