Hilbert coefficients of Hilbert filtrations
type: Item
instance of: scholarly article
title: Hilbert coefficients of Hilbert filtrations
zbMATH Open document ID: 0899.13017
published in: Journal of Algebra
publication date: 1998-03-24T00:00:00Z
review text: This paper deals with the Hilbert series of a Hilbert filtration \({\mathcal F}\) in a local ring \((A,m)\); its aim is to study the Hilbert function and the Hilbert coefficients of \({\mathcal F}\). Many results already known for the \(I\)-adic case are extended to this more general one: In particular, the Cohen-Macaulay property of \(gr_{\mathcal F} (A)\) is characterized in terms of lower bound of \(e_1 ({\mathcal F})\). The last part of the paper is devoted to the case of a \(I\)-adic filtration, with \(I\) an \(m\)-primary ideal in a local Cohen-Macaulay ring: The behaviour of the Hilbert function is described when some extremal conditions are satisfied by Hilbert coefficients, generalizing results already known in more special cases.
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13H15
zbMATH DE Number: 1115981
zbMATH Keywords: Hilbert series
zbMATH Keywords: Hilbert filtration
zbMATH Keywords: Hilbert coefficients
zbMATH Keywords: Hilbert function
author: Anna Guerrieri
author: M. E. Rossi
reviewed by: Carla Massaza
MaRDI profile type: Publication
full work available at URL: jabr.1997.7194
OpenAlex ID: W2007947254
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DOI: 10.1006/JABR.1997.7194
description: scientific article; zbMATH DE number 1115981