Counting Finite-Dimensional Algebras Over Finite Field

Nikolaas D. Verhulst

doi:10.1007/s00025-020-01281-6

Counting Finite-Dimensional Algebras Over Finite Field

Nikolaas D. Verhulst

Discrete Mathematics and Optimization

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Abstract

In this paper, we describe an elementary method for counting the number of non-isomorphic algebras of a fixed, finite dimension over a given finite field. We show how this method works in the case of 2-dimensional algebras over the field F₂.

Original language	English
Article number	153
Pages (from-to)	1-9
Number of pages	9
Journal	Results in Mathematics
Volume	75
Issue number	4
DOIs	https://doi.org/10.1007/s00025-020-01281-6
Publication status	Published - 2020

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Counting Finite-Dimensional Algebras Over Finite Field

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