P.I. degree of tensor products of PI-algebras
type: Item
instance of: scholarly article
title: P.I. degree of tensor products of PI-algebras
zbMATH Open document ID: 0673.16011
DOI: 10.1016/0021-8693(89)90035-5
author: Tatiana Gateva
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let A be an associative algebra with 1 over a fixed field F of characteristic zero and \(M_ n\) be the algebra of all \(n\times n\) matrices over the field F. By n(A) is denoted the maximal integer n for which every polynomial identity of A also is an identity of \(M_ n.\) In this paper the author investigates the dependence between n(A), n(B) and n(A\(\otimes B)\) and proves that for arbitrary PI-algebras A and B the inequality n(A\(\otimes B)\leq 2n(A)n(B)\) holds and this upper bound for n(A\(\otimes B)\) is sharp, where \(A\otimes B\) is the tensor product of A and B taken over F. The lower bound n(A\(\otimes B)\geq n(A)n(B)\) for n(A\(\otimes B)\) which also is sharp has been established by the author [in Vestn. Mosk. Univ., Ser. I 1980, No.2, 47-50 (1980; Zbl 0429.16014)]. In the paper reviewed she gives a characterization of PI-algebras A with the property that for every PI-algebra B the equality \(n(A)n(B)=n(A\otimes B)\) holds.
Mathematics Subject Classification ID: 16Rxx
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 4101395
zbMATH Keywords: P.I. degree
zbMATH Keywords: algebra of matrices
zbMATH Keywords: polynomial identity
zbMATH Keywords: PI-algebras
zbMATH Keywords: tensor product
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90035-5
OpenAlex ID: W2026196316
cites work: The T -Ideals of the Free Ring
cites work: Q3866230
cites work: Q3325875
cites work: Polynomial identities of related rings
cites work: Existence of identities in \(A \otimes B\)
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description: scientific article; zbMATH DE number 4101395