On the semiprimitivity of finitely generated algebras

Okniński, Jan

doi:10.1090/S0002-9939-2014-12187-3

On the semiprimitivity of finitely generated algebras
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by Jan Okniński

Proc. Amer. Math. Soc. 142 (2014), 4095-4098

DOI: https://doi.org/10.1090/S0002-9939-2014-12187-3

Published electronically: August 18, 2014

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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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