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arXiv · 1608.00926

Nonnoetherian coordinate rings with unique maximal depictions

Charlie Beil
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Abstract

A depiction of a nonnoetherian integral domain $R$ is a special coordinate ring that provides a framework for describing the geometry of $R$. We show that if $R$ is noetherian in codimension 1, then $R$ has a unique maximal depiction $T$. In this case, the geometric dimensions of the points of $\operatorname{Spec}R$ may be computed directly from $T$. If in addition $R$ has a normal depiction $S$, then $S$ is the unique maximal depiction of $R$.

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Charlie Beil. 2016-08-02. Nonnoetherian coordinate rings with unique maximal depictions. https://arxiv.org/abs/1608.00926

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