# The representations ofSnand explicit identities for P. I. algebras

- Authors
- Journal
- Journal of Algebra 0021-8693
- Publisher
- Elsevier
- Publication Date
- Volume
- 51
- Issue
- 1
- Identifiers
- DOI: 10.1016/0021-8693(78)90133-3
- Disciplines

## Abstract

Abstract The representation theory of S n is applied to prove that for any P.I. algebra, FS n contains a certain two-sided ideal of identities, provided that n is big enough. In characteristic zero this yields Amitsur's s l k [ x] theorem together with explicit l and k. The same methods yield an explicit identity for A ⊗ B. Modular representations of S n are used to extend those results to an arbitrary characteristic.

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