The Hilbert series of prime PI rings.
type: Item
instance of: scholarly article
title: The Hilbert series of prime PI rings.
zbMATH Open document ID: 1068.16025
DOI: 10.1007/BF02787539
author: Jason P. Bell
published in: Israel Journal of Mathematics
publication date: 2004-11-11T00:00:00Z
review text: Let \(A\) be an algebra generated over a field \(k\) by a finite dimensional vector space \(V\) with \(1\in V\). The Hilbert series of \(A\) with respect to \(V\) is defined as \(1+\sum_{n\geq 1}\dim(V^n/V^{n-1})t^n\). The main result of the paper under review is that if \(A\) is a finitely generated prime PI-algebra, then its Hilbert series is rational for a suitable generating subspace. Together with the theory of PI-algebras, the proof uses ideas from the theory of noncommutative Gröbner bases.
reviewed by: Vesselin Drensky
Mathematics Subject Classification ID: 16R20
Mathematics Subject Classification ID: 16S15
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16P90
zbMATH DE Number: 2114519
zbMATH Keywords: rings with polynomial identity
zbMATH Keywords: prime algebras
zbMATH Keywords: rational Hilbert series
zbMATH Keywords: Gelfand-Kirillov dimension
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2114519