Reduction in Rees algebra of modules
type: Item
instance of: scholarly article
title: Reduction in Rees algebra of modules
zbMATH Open document ID: 1360.13015
author: Priti Singh
author: Shiv Datt Kumar
published in: Algebras and Representation Theory
publication date: 2015-01-07T00:00:00Z
review text: \textit{P. Eakin} and \textit{A. Sathaye} [J. Algebra 41, 439--454 (1976; Zbl 0348.13012)] proved that if \(I\) is an ideal in the local ring \(R\) with infinite residue field such that \(I^n\) can be generated by fewer than \(n+r \choose r\) elements, for some integers \(n\geq 1\) and \(r\geq 0\), then there are elements \(y_1,\dots,y_r\) in \(I\), such that \((y_1,\dots, y_r )I^{n-1}=I^n\). In the paper under review, the authors generalize a Eakin-Sathaye theorem for more general class of algebras (Rees Algebras) through application of Zariski open sets associated with the reductions for the Rees algebra of modules.
reviewed by: Amir Mafi
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 6384238
zbMATH Keywords: reduction of modules
zbMATH Keywords: Rees algebra of modules
zbMATH Keywords: fiber cone
MaRDI profile type: Publication
full work available at URL: s10468-014-9471-1
OpenAlex ID: W1990157270
cites work: Q5563439
cites work: The Buchsbaum-Rim polynomial of a module
cites work: Around the Eakin-Sathaye theorem
cites work: On the asymptotic properties of the Rees powers of a module
cites work: On Equimultiple Modules
cites work: Prestable ideals
cites work: What is the Rees algebra of a module?
cites work: Specialization of integral dependence for modules
cites work: Borel-fixed ideals and reduction number.
cites work: Reduction criteria for modules
cites work: Symmetric powers of complete modules over a two-dimensional regular local ring
cites work: The core of a module over a two-dimensional regular local ring
cites work: Q5829838
cites work: Q4694069
cites work: Reduction of modules
cites work: Rees Algebras of Modules
cites work: Q3414477
cites work: Q4680541
DOI: 10.1007/S10468-014-9471-1
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description: scientific article; zbMATH DE number 6384238