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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



An application of representation theory to PI-algebras

Authors: Jørn B. Olsson and Amitai Regev
Journal: Proc. Amer. Math. Soc. 55 (1976), 253-257
MathSciNet review: 0399154
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Abstract: By realizing that the multilinear identities of degree $ n$ of a $ PI$-algebra form a left ideal in the group algebra $ F[{S_n}]$, it is possible sometimes to use the representation theory of the symmetric group $ {S_n}$ in the study of $ T$-ideals and $ PI$-algebras. In this note we demonstrate this method by proving: Theorem. If the codimensions of a $ PI$-algebra are bounded, then they are eventually bounded by $ 1$.

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Article copyright: © Copyright 1976 American Mathematical Society