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09 February 2025
 
  » arxiv » 1609.0089

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Quadratic Generated Normal Domains From Graphs
Drew J. Lipman ; Michael A. Burr ;
Date 1 Sep 2016
AbstractDetermining whether an arbitrary subring $R$ of $k[x_1^{pm 1},ldots, x_n^{pm 1}]$ is a normal domain is, in general, a nontrivial problem, even in the special case of a monomial generated domain. In this paper, we consider the case where $R$ is a quadratic-monomial generated domain. For the ring $R$, we consider the combinatorial structure that assigns an edge in a mixed directed signed graph to each monomial of the ring. In this paper we use this relationship to provide a combinatorial characterization of the normality of $R$, and, when $R$ is not normal, we use the combinatorial characterization to compute the normalization of $R$.
Source arXiv, 1609.0089
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