Quasi-one-fibered and projectively full ideals in 2-dimensional Muhly rational singularities
type: Item
instance of: scholarly article
title: Quasi-one-fibered and projectively full ideals in 2-dimensional Muhly rational singularities
zbMATH Open document ID: 1360.13023
author: Veronique Van Lierde
published in: European Journal of Mathematics
publication date: 2017-01-11T00:00:00Z
review text: \((R, m)\) is assumed to be a 2-dimensional Muhly rational singularity, a class that contains a 2-dimensional regular local rings. The main result is as follows (in order to simplify the formulation \( m\) is assumed to be the quasi-one-fibered ideal associated with ord\(_R\): Let \(I\) be a complete \( m\)-primary ideal of \(R\), let \(T(I)=\{v_i,\dots, v_n\}\) and let \(I_i\) be the quasi-one-fibered ideal associated with \(v_i\), \(i=1,\dots,n\). Then there exist natural numbers \(s, u_1,\dots,u_n\), such that Im\(^s=I_1^{u_1}\cdot\cdot\cdot I_n^{u_n}\). We mention another noteworthy result: If \((R, m)\) is a 2-dimensional Muhly rational singularity, then \(R\) is regular, if and only if, then for every complete \( m\)-primary ideal \(I\) of \(R\), there exist positive integers \(e_i\), such that \(I=A_{v_1}^{e_1}\cdot\cdot\cdot A_{v_n}^{e_n}\). Here the ideals \(A_{v_i}\) are the one-fibered ideals associated with the Rees valuation of \(I\)).
reviewed by: Radoslav M. Dimitrić
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 6673769
zbMATH Keywords: degree function
zbMATH Keywords: Rees valuation
zbMATH Keywords: complete ideal
zbMATH Keywords: 2-dimensional rational singularity
zbMATH Keywords: quasi-one-fibered ideal
zbMATH Keywords: projectively full ideal
MaRDI profile type: Publication
full work available at URL: s40879-016-0105-5
OpenAlex ID: W2342024611
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DOI: 10.1007/S40879-016-0105-5
description: scientific article; zbMATH DE number 6673769