Analytically unramified one-dimensional semilocal rings and their value semigroups
type: Item
instance of: scholarly article
title: Analytically unramified one-dimensional semilocal rings and their value semigroups
zbMATH Open document ID: 0963.13021
DOI: 10.1016/S0022-4049(98)00160-1
author: Valentina Barucci
author: M. D'Anna
author: Ralf Fröberg
published in: Journal of Pure and Applied Algebra
publication date: 2001-06-22T00:00:00Z
review text: 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.
reviewed by: Gerhard Pfister
Mathematics Subject Classification ID: 13H99
Mathematics Subject Classification ID: 13A18
zbMATH DE Number: 1435988
zbMATH Keywords: valuation on semigroup of a ring
zbMATH Keywords: normalisation
zbMATH Keywords: one-dimensional ring
zbMATH Keywords: maximal embedding dimension
zbMATH Keywords: almost Gorenstein rings
zbMATH Keywords: Arf ring
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1435988