Nonnoetherian coordinate rings with unique maximal depictions

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 $\mathrm{Spec}R$ may be computed directly from $T$. If in addition $R$ has a normal depiction $S$, then $S$ is the unique maximal depiction of $R$.

15 pages. To appear, Communications in Algebra