Quasi-one-fibered ideals in two-dimensional Muhly local domains
type: Item
instance of: scholarly article
title: Quasi-one-fibered ideals in two-dimensional Muhly local domains
zbMATH Open document ID: 1271.13019
author: Raymond Debremaeker
published in: Journal of Algebra
publication date: 2012-03-22T00:00:00Z
review text: A two-dimensional local ring \((R,M)\) is called a Muhly domain, if it is a two-dimensional normal Noetherian local domain with algebraically closed residue field and with the associated graded ring an integrally closed domain. The \(M\)-adic order function \(\mathrm{ord}_R\) of a Muhly domain is a valuation denoted by \(v_M\). The set of all Rees valuations of an \(M\)-primary ideal \(I\) is denoted by \(T(I)\). An \(M\)-primary ideal \(I\) is called quasi-one-fibered, if \(T (I) \subset \{v_M, w\}\) and \(w\in T (I)\) where \(w\) denotes a prime divisor not equal with \(v_M\). The paper is about of the degree function coefficients of quasi-one-fibered \(M\)-primary ideals in two-dimensional Muhly local domains.
reviewed by: Mohsen Asgharzadeh
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 6017052
zbMATH Keywords: degree function
zbMATH Keywords: complete ideal
zbMATH Keywords: Muhly local domain
zbMATH Keywords: Rees valuation
zbMATH Keywords: quasi-one-fibered ideal
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2011.07.028
OpenAlex ID: W1992326296
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DOI: 10.1016/J.JALGEBRA.2011.07.028
description: scientific article; zbMATH DE number 6017052