- PII
- 10.31857/S0132347424020115-1
- DOI
- 10.31857/S0132347424020115
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume / Issue number 2
- Pages
- 84-92
- 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.
- Keywords
- шрайерово многообразие линейных алгебр свободные неассоциативные алгебры примитивные элементы свободных алгебр свободное дифференциальное исчисление в свободных алгебрах
- Date of publication
- 15.04.2024
- Year of publication
- 2024
- Number of purchasers
- 0
- Views
- 31
References
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