Analytically unramified one-dimensional semilocal rings and their value semigroups
Let \((R,m)\) be a one-dimensional semi-local ring such that the integral closure is a finite \(R\)-module. Let \(\Gamma(R) \subset \mathbb N^d\) be the semigroup of values of \(R\). Properties of the semigroup are studied and related to the corresponding properties of the ring. Especially Gorenstein rings, Arf rings and rings of small multiplicity are treated. For instance, almost Gorenstein rings and rings of maximal embedding dimension are characterised in terms of the semigroup.
scientific article; zbMATH DE number 1435988