Reduction numbers and multiplicities of multigraded structures
type: Item
instance of: scholarly article
title: Reduction numbers and multiplicities of multigraded structures
zbMATH Open document ID: 0931.13002
author: Manfred Herrmann
author: Eero Hyry
author: Jürgen Ribbe
author: Zhongming Tang
published in: Journal of Algebra
publication date: 2000-02-23T00:00:00Z
review text: Let \(A\) be a local ring and let \(I_1,\dots,I_r\) be ideals in \(A\). The multi-Rees algebra with respect to \(I_1,\dots ,I_r\) is the ring \(R_A(I_1,\dots,I_r) = A[I_1t_1,\dots,I_rt_r]\) where \(t_1,\dots,t_r\) are indeterminates, and the multiform rings are the rings \(\text{gr}_A(I_1,\dots,I_r;I_i)= R_A(I_1,\dots,I_r)/I_iR_A(I_1,\dots,I_r)\), \(i=1,\dots,r\). We quote from the authors' introduction: The aim of this paper is twofold. First we want to relate the Cohen-Macaulay property of \(R_A(I_1,\dots,I_r)\) to the Cohen-Macaulay property of the ordinary Rees rings \(R_A(I_j)\) \((j = 1,\dots,r)\). Then we determine the multiplicities of multi-Rees and form rings. In particular, we ask when minimal multiplicity occurs.
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13H15
zbMATH DE Number: 1104102
zbMATH Keywords: multiplicity
zbMATH Keywords: multi-Rees algebra
zbMATH Keywords: multiform rings
zbMATH Keywords: Cohen-Macaulay property
reviewed by: Udo Vetter
MaRDI profile type: Publication
full work available at URL: jabr.1997.7128
OpenAlex ID: W2153297616
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DOI: 10.1006/JABR.1997.7128
description: scientific article; zbMATH DE number 1104102