On PI-subrings of matrix rings over some classes of skew fields
type: Item
instance of: scholarly article
title: On PI-subrings of matrix rings over some classes of skew fields
zbMATH Open document ID: 0656.16007
DOI: 10.1016/0022-4049(88)90136-3
author: A. I. Lichtman
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let \(\Delta\) be either the (skew) field of fractions of a group ring KG, where G is a torsion free nilpotent group, or the universal field of fractions of a free group ring, or the universal field of fractions of a group ring of a free soluble group, or else the universal enveloping algebra of a finite-dimensional Lie algebra over a field of characteristic zero. It is proved that if \(D_{k\times k}\) is a matrix subring of \(\Delta_{n\times n}\) where D is a field of dimension \(m^ 2\) over its center, then the PI-degree of \(D_{k\times k}\) divides n (see Corollary 1.3). It is a generalization of Schofield's (1985) result which states that if E is a subfield of \(\Delta_{n\times n}\) where \(\Delta\) is the universal field of fractions of a free group ring, then the PI-degree of E divides n.
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16Rxx
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 16Kxx
zbMATH DE Number: 4071126
zbMATH Keywords: skew field
zbMATH Keywords: group ring
zbMATH Keywords: torsion free nilpotent group
zbMATH Keywords: universal field of fractions
zbMATH Keywords: free group ring
zbMATH Keywords: free soluble group
zbMATH Keywords: universal enveloping algebra
zbMATH Keywords: matrix subring
zbMATH Keywords: PI-degree
reviewed by: Leonid A. Bokut'
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90136-3
OpenAlex ID: W1968701999
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description: scientific article; zbMATH DE number 4071126