Cohen-Macaulay and Gorenstein property of Rees algebras of non-singular equimultiple prime ideals
type: Item
instance of: scholarly article
title: Cohen-Macaulay and Gorenstein property of Rees algebras of non-singular equimultiple prime ideals
zbMATH Open document ID: 0758.13004
DOI: 10.1007/BF02567752
author: Trung Ngo Viet
author: Duong Quoc Viet
published in: Manuscripta Mathematica
publication date: 1993-01-17T00:00:00Z
full work available at URL: https://eudml.org/doc/155745
review text: The main purpose of this paper is to study the problem when the Rees algebra \(R({\mathfrak p})\) of a height 2 non-singular equimultiple prime ideal \({\mathfrak p}\) of some local ring \(A\) is a Cohen-Macaulay, respectively Gorenstein ring. The paper deals with the conjecture, which asserts that the Gorenstein property of \(R({\mathfrak p})\) implies that of \(A\) when \(\dim A=3\), the case \(\dim A\geq 4\) having been settled positively by Herrmann and Ikeda. Note that the analogous question for the Cohen-Macaulay property has been proven to have a negative answer by Hermann, Ribbe and the first named author. Here it is shown (besides a thorough study of the CM and Gorenstein problem in arbitrary characteristic) that the conjecture has a positive answer if \(\text{char }K\neq 2\) and if \(v(p)\leq 3\), where \(v(p)\) is the minimal number of generators of \(p\), whereas counterexamples may be given otherwise.
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 97888
zbMATH Keywords: Rees algebra
zbMATH Keywords: Cohen-Macaulay property
zbMATH Keywords: Gorenstein problem
MaRDI profile type: Publication
cites work: On Serre's conditions in the form ring of an ideal
cites work: The Gorenstein property depends on characteristic
cites work: On the Gorenstein property of Rees algebras
cites work: Q4040095
cites work: Rees algebras of non-singular equimultiple prime ideals
cites work: On the canonical module of the Rees algebra and the associated graded ring of an ideal
cites work: The Gorenstein property depends upon characteristic for affine semigroup rings
cites work: Five theorems on Macaulay rings
cites work: The theory of d-sequences and powers of ideals
cites work: On the associated graded ring of an ideal
cites work: On the Gorensteinness of Rees algebras over local rings
cites work: Remarks on lifting of Cohen-Macaulay property
cites work: When is the rees algebra cohen—macaulay?
cites work: Q5829838
cites work: Cohen-Macaulay quotients of polynomial rings
cites work: Über die Übertragung der Ringeigenschaften zwischenR undR[u]/(F)
cites work: From associated graded modules to blowing-ups of generalized Cohen-Macaulay modules
cites work: Reduction Exponent and Degree Bound for the Defining Equations of Graded Rings
OpenAlex ID: W2002215217
description: scientific article; zbMATH DE number 97888