Primitive elements of free non-associative algebras over finite fields
- 作者: Maisuradze M.1, Mikhalev А.1
-
隶属关系:
- Moscow State University
- 期: 编号 2 (2024)
- 页面: 84-92
- 栏目: 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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详细
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.
作者简介
M. Maisuradze
Moscow State University
编辑信件的主要联系方式.
Email: maisuradzemv@my.msu.ru
Department of Mechanics and Mathematics
俄罗斯联邦, Moscow, 119991А. Mikhalev
Moscow State University
Email: aamikhalev@mail.ru
Department of Mechanics and Mathematics
俄罗斯联邦, Moscow, 119991参考
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