Domains with linear growth
type: Item
instance of: scholarly article
title: Domains with linear growth
zbMATH Open document ID: 0806.16023
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1995-02-15T00:00:00Z
full work available at URL: https://eudml.org/doc/229992
review text: Let \(A\) be an affine \(k\)-algebra, \(k\) a field, and \(V\) a finite dimensional \(k\)-subspace of \(A\) that contains 1 and a set of generators of \(A\). The ``growth'' of \(A\) (relative to \(V\)) is said to be bounded by a linear polynomial if there exists a constant \(c\) such that \(f(n) \leq cn\) for all \(n\). In the paper it is shown that an affine \(k\)-algebra \(R\) that is a domain with growth bounded by a linear polynomial satisfies a polynomial identity and hence is a finite module over its center.
reviewed by: Jan Van Geel
Mathematics Subject Classification ID: 16P90
Mathematics Subject Classification ID: 16R10
Mathematics Subject Classification ID: 16U10
Mathematics Subject Classification ID: 16S15
zbMATH DE Number: 589780
zbMATH Keywords: growth bounded by linear polynomial
zbMATH Keywords: finite module over center
zbMATH Keywords: affine \(k\)-algebra
zbMATH Keywords: generators
zbMATH Keywords: domain
zbMATH Keywords: polynomial identity
author: T. H. Lenagan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 589780