Matrix representability of finitely-generated PI-algebras
type: Item
instance of: scholarly article
title: Matrix representability of finitely-generated PI-algebras
zbMATH Open document ID: 0711.16017
published in: Moscow University Mathematics Bulletin
publication date: 1989-01-01T00:00:00Z
review text: It is proved that a finitely generated unital PI-algebra containing only one left annihilator is representable (i.e. can be imbedded into a matrix ring over some commutative algebra). On the other hand the author constructs an example of a nonrepresentable finitely generated unital PI- algebra containing exactly two left annihilators and satisfying the quasi-identities \[ \bigwedge_{0\leq p\leq 4}(\sum^{s}_{j=1}a_ jx^ pb_ j=0)\quad \Rightarrow \quad \sum^{s}_{j=1}a_ jx^ 4b_ j=0,\quad s=1,2,...\quad. \]
Mathematics Subject Classification ID: 16R20
Mathematics Subject Classification ID: 16R50
zbMATH DE Number: 4168887
zbMATH Keywords: finitely generated unital PI-algebra
zbMATH Keywords: left annihilator
zbMATH Keywords: matrix ring
zbMATH Keywords: nonrepresentable finitely generated unital PI-algebra
zbMATH Keywords: quasi-identities
author: Victor Markov
reviewed by: Ivan Shestakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4168887