On the Gorenstein property of Rees algebras
type: Item
instance of: scholarly article
title: On the Gorenstein property of Rees algebras
zbMATH Open document ID: 0641.13013
DOI: 10.1007/BF01170849
published in: Manuscripta Mathematica
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155262
review text: Let (A,m) be a local Noetherian ring, and let P be prime ideal of A whose height and analytic spread are equal. Let R(P) be the Rees ring \(\oplus P^ n,\quad n\geq 0\). The authors consider what the Gorensteinness of R(P) implies about R and P. Theorem: If (A,m) is a generalized Cohen- Macaulay ring (i.e., a ring of finite local cohomology) with Dim(A)\(\geq 4\), if height(P) \(= analytic\) spread \(of\quad P =2,\) and if R(P) is Gorenstein, then P is generated by a regular sequence, and A is Gorenstein. In the case that \(Dim(A)=3\), the authors conjecture that the theorem remains true, and prove it in cases in which the multiplicity of A is small. The final section of the paper treats the case that \(P=m\).
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13H15
zbMATH DE Number: 4043977
zbMATH Keywords: local Noetherian ring
zbMATH Keywords: height
zbMATH Keywords: analytic spread
zbMATH Keywords: Rees ring
zbMATH Keywords: Gorensteinness
zbMATH Keywords: generalized Cohen-Macaulay ring
zbMATH Keywords: multiplicity
author: Manfred Herrmann
author: Shin S. Ikeda
MaRDI profile type: Publication
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OpenAlex ID: W2014607015
description: scientific article; zbMATH DE number 4043977