On equimultiple ideals
type: Item
instance of: scholarly article
title: On equimultiple ideals
zbMATH Open document ID: 0811.13017
DOI: 10.1007/BF02571697
author: Kishor Shah
published in: Mathematische Zeitschrift
publication date: 1994-05-31T00:00:00Z
full work available at URL: https://eudml.org/doc/174596
review text: The following typifies the nature of the results: Let \(R\) be a local ring with maximal ideal \(M\). Let \(I\) and \(J\) be ideals such that \(I+J\) is \(M\)- primary. Let \(G(I) = \bigoplus^ \infty_{s=0} I^ s/I^{s+1}\) be the associated graded ring. Then: (a) \(G(I) \otimes_ R G(J)\) has dimension \(d+g\) where \(d, g\) are the analytic spreads of \(I, J\) respectively. (b) If \(I\) and \(J\) are analytically disjoint ideals, each generated by regular sequences, then the tensor ring \(G(I) \otimes_ R G(J)\) is a Cohen-Macaulay ring of dimension \(\dim R\). (c) If \(I\) and \(J\) are analytically disjoint ideals such that \(I + J = M\), with \(I\) containing \(X\) such that \(I^ 2 = IX\), and \(J\) containing \(Y\) such that \(J^ 2 = JY\) with each of \(X\) and \(Y\) being generated by regular sequences, then \(G(I) \otimes_ R G(J)\) is Cohen-Macaulay of dimension \(\dim R\).
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13A30
zbMATH DE Number: 567416
zbMATH Keywords: equimultiple ideal
zbMATH Keywords: Cohen-Macaulayness
zbMATH Keywords: associated graded ring
zbMATH Keywords: analytic spreads
reviewed by: K. Chandrasekhara Rao
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 567416