Email this article Primitive elements of free non-associative algebras over finite fields
- Authors: Maisuradze M.V.1, Mikhalev А.А.1
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Affiliations:
- Moscow State University
- Issue: No 2 (2024)
- Pages: 84-92
- Section: КОМПЬЮТЕРНАЯ АЛГЕБРА
- URL: https://journals.rcsi.science/0132-3474/article/view/262652
- DOI: https://doi.org/10.31857/S0132347424020115
- EDN: https://elibrary.ru/RODPXT
- ID: 262652
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Abstract
The representation of elements of free non-associative algebras as a set of multidimensional tables of coefficients is defined. An operation for finding partial derivatives for elements of free non-associative algebras in the same form is considered. Using this representation, a criterion of primitivity for elements of lengths 2 and 3 in terms of matrix ranks, as well as a primitivity test for elements of arbitrary length, is derived. This test makes it possible to estimate the number of primitive elements in free non-associative algebras with two generators over a finite field. The proposed representation allows us to optimize algorithms for symbolic computations with primitive elements. Using these algorithms, we find the number of primitive elements of length 4 in a free non-associative algebra of rank 2 over a finite field.
About the authors
M. V. Maisuradze
Moscow State University
Author for correspondence.
Email: maisuradzemv@my.msu.ru
Department of Mechanics and Mathematics
Russian Federation, Moscow, 119991А. А. Mikhalev
Moscow State University
Email: aamikhalev@mail.ru
Department of Mechanics and Mathematics
Russian Federation, Moscow, 119991References
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