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On the semiprimitivity of finitely generated algebras


Author: Jan Okniński
Journal: Proc. Amer. Math. Soc. 142 (2014), 4095-4098
MSC (2010): Primary 16S15, 16N20; Secondary 16S36, 20M25, 68Q70
DOI: https://doi.org/10.1090/S0002-9939-2014-12187-3
Published electronically: August 18, 2014
MathSciNet review: 3266980
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Abstract: Finitely generated associative algebras $ A=K\langle a_{1},\ldots , a_{n}\rangle $ over a field $ K$ defined by homogeneous relations are considered. If there exists an order on the associated free monoid $ \mathrm {FM}_{n}$ of rank $ n$ such that the set of normal forms of elements of $ A$ is a regular language in $ \mathrm {FM}_{n}$, then the algebra $ A$ is semiprimitive provided that the associated monomial algebra is semiprime.


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Additional Information

Jan Okniński
Affiliation: Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland
Email: okninski@mimuw.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-2014-12187-3
Received by editor(s): April 11, 2012
Received by editor(s) in revised form: February 1, 2013
Published electronically: August 18, 2014
Additional Notes: This work was supported by MNiSW research grant N201 420539
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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