On the deviation and the type of certain local Cohen-Macaulay rings and numerical semigroups
type: Item
instance of: scholarly article
title: On the deviation and the type of certain local Cohen-Macaulay rings and numerical semigroups
zbMATH Open document ID: 1393.13044
author: R. Waldi
author: E. Kunz
published in: Journal of Algebra
publication date: 2017-03-16T00:00:00Z
review text: Let \(R\) be a Noetherian local ring and \(\hat{R}=P/I\), where \(\hat{R}\) is the completion of \(R\) and \(P\) is a regular local ring. Let \(\mu(I)\) be the minimal number of generators of \(I\), then the number \(d(R):=\mu(I)-(\dim(P)-\dim(R))\) is independent of the chosen presentation of \(\hat{R}\) and is called the deviation of \(R\). In this article under review, the authors study certain Cohen-Macaulay rings for which there are close relations between deviation, type and embedding dimension. This relations apply to numerical semigroups (or equivalently monomial curves) and lead also to some further cases, generalizing [\textit{E. Kunz}, Semigroup Forum 93, No. 1, 205--210 (2016; Zbl 1347.20069)] with ring-theoretic proofs, in which a question of \textit{H. S. Wilf} [Am. Math. Mon. 85, 562--565 (1978; Zbl 0387.10009)] has a positive answer.
reviewed by: Amir Mafi
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 20M14
zbMATH DE Number: 6695610
zbMATH Keywords: Cohen-Macaulay ring
zbMATH Keywords: deviation
zbMATH Keywords: type
zbMATH Keywords: embedding dimension
zbMATH Keywords: numerical semigroup
zbMATH Keywords: geometrical illustration
zbMATH Keywords: relation ideal
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2017.01.041
OpenAlex ID: W2583983111
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DOI: 10.1016/J.JALGEBRA.2017.01.041
description: scientific article; zbMATH DE number 6695610