The standard identity in characteristic \(p\): A conjecture of I. B. Volichenko
type: Item
instance of: scholarly article
title: The standard identity in characteristic \(p\): A conjecture of I. B. Volichenko
zbMATH Open document ID: 0795.16017
DOI: 10.1007/BF02764837
published in: Israel Journal of Mathematics
publication date: 1993-09-07T00:00:00Z
review text: The main result of this interesting paper is to answer in the affirmative the conjecture of I. B. Volichenko that any PI-algebra over a field of positive characteristic satisfies the standard identity. This means (in contrast to the case of characteristic 0) that in positive characteristic the standard identity cannot be used for the characterization of the \(T\)- ideals of the identities satisfied by a finitely generated algebra. As a consequence of the proof the author establishes the nice result that any PI-algebra over a field of positive characteristic satisfies the same multilinear polynomial identities as some nil-algebra of bounded index.
Mathematics Subject Classification ID: 16R10
Mathematics Subject Classification ID: 16R50
Mathematics Subject Classification ID: 16N40
Mathematics Subject Classification ID: 16S10
zbMATH DE Number: 410022
zbMATH Keywords: characteristic \(p\)
zbMATH Keywords: standard identity
zbMATH Keywords: \(T\)-ideals
zbMATH Keywords: finitely generated algebra
zbMATH Keywords: PI-algebra
zbMATH Keywords: multilinear polynomial identities
zbMATH Keywords: nil-algebra of bounded index
Wikidata QID: Q123229961
author: Alexander Kemer
reviewed by: Vesselin Drensky
MaRDI profile type: Publication
cites work: IDENTITIES OF FINITELY GENERATED ALGEBRAS OVER AN INFINITE FIELD
full work available at URL: https://doi.org/10.1007/bf02764837
OpenAlex ID: W1971988543
description: scientific article; zbMATH DE number 410022