On the length equalities for one-dimensional rings
type: Item
instance of: scholarly article
title: On the length equalities for one-dimensional rings
zbMATH Open document ID: 1107.13027
published in: Journal of Pure and Applied Algebra
publication date: 2006-03-29T00:00:00Z
review text: Let \(R\) be a noetherian local one-dimensional analytically irreducible and residual rational domain which is not Gorenstein. Let \(\ell^*(R) = \tau_R\ell(R/C)-\ell(\overline R/R)\), where \(\tau_R\) is the Cohen-Macaulay type of \(R\), \(C\) is the conductor of \(R\) in the integral closure \(\overline R\). In this paper, the authors characterize the rings \(R\) with \(\ell^*(R) = \tau_R-1\) and \(\ell(R/C+xR) = 2\), where \(xR\) is a minimal reduction of the maximal ideal, by means of the numerical semigroup of \(R\). Moreover, they also give a characterization of almost Gorenstein semigroup rings \(R\) with \(\ell^*(R) = \tau_R-1\).
reviewed by: Trung Ngo Viet
Mathematics Subject Classification ID: 13H15
Mathematics Subject Classification ID: 13B22
zbMATH DE Number: 5016244
zbMATH Keywords: one-dimensional local domain
zbMATH Keywords: conductor
zbMATH Keywords: minimal reduction
author: Dilip P. Patil
author: Grazia Tamone
MaRDI profile type: Publication
full work available at URL: j.jpaa.2005.07.005
OpenAlex ID: W2050318678
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DOI: 10.1016/J.JPAA.2005.07.005
description: scientific article; zbMATH DE number 5016244