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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

PI semigroup algebras of linear semigroups


Authors: Jan Okniński and Mohan S. Putcha
Journal: Proc. Amer. Math. Soc. 109 (1990), 39-46
MSC: Primary 20M25; Secondary 16A38, 16A45, 20M20
MathSciNet review: 1013977
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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$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1013977-4
PII: S 0002-9939(1990)1013977-4
Article copyright: © Copyright 1990 American Mathematical Society