Malaysian Journal of Mathematical Sciences, September 2022, Vol. 16, No. 3
Canonical Form Algorithm and Separating Systems for Two-Dimensional Algebras
Ahmed, H., Bekbaev, U., and Rakhimov, I.
Corresponding Email: isamiddin@uitm.edu.my
Received date: 5 May 2021
Accepted date: 21 July 2022
Abstract:
For a field $\mathbb{F}$, where any polynomial of degree two and three possess a root, we give an
algorithm transforming any two-dimensional algebra over $\mathbb{F}$ to a "canonical form" in terms of
structure constants of the algebra. A system of invariant conditions in form of equalities and non-equalities
(inequalities) separating non-isomorphic two-dimensional algebras is given.
Keywords: algebra; invariant; matrix of structure constants; canonical form
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