PI semigroup algebras of linear semigroups
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- by Jan Okniński and Mohan S. Putcha PDF
- Proc. Amer. Math. Soc. 109 (1990), 39-46 Request permission
Abstract:
It is well-known that if a semigroup algebra $K[S]$ over a field $K$ satisfies a polynomial identity then the semigroup $S$ has the permutation property. The converse is not true in general even when $S$ is a group. In this paper we consider linear semigroups $S \subseteq {\mathcal {M}_n}(F)$ having the permutation property. We show then that $K[S]$ has a polynomial identity of degree bounded by a fixed function of $n$ and the number of irreducible components of the Zariski closure of $S$.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 39-46
- MSC: Primary 20M25; Secondary 16A38, 16A45, 20M20
- DOI: https://doi.org/10.1090/S0002-9939-1990-1013977-4
- MathSciNet review: 1013977