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Primitive Elements of Free Non-associative Algebras over Finite Fields.
- Source :
-
Programming & Computer Software . Apr2024, Vol. 50 Issue 2, p180-187. 8p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03617688
- Volume :
- 50
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Programming & Computer Software
- Publication Type :
- Academic Journal
- Accession number :
- 177392714
- Full Text :
- https://doi.org/10.1134/S0361768824020117