A Classification of Two-dimensional Endo-commutative Algebras over F_2

Sin-Ei Takahasi; Kiyoshi Shirayanagi; Makoto Tsukada

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arXiv · 2211.04015

A Classification of Two-dimensional Endo-commutative Algebras over F_2

Sin-Ei Takahasi·Kiyoshi Shirayanagi·Makoto Tsukada

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Abstract

We introduce a new class of algebras called endo-commutative algebras in which the square mapping preserves multiplication, and provide a complete classification of endo-commutative algebras of dimension 2 over the field F_2 of two elements. We list all multiplication tables of the algebras up to isomorphism. This clarifies the difference between commutativity and endo-commutativity of algebras.

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BibTeX RIS

Sin-Ei Takahasi, Kiyoshi Shirayanagi, Makoto Tsukada. 2022-11-08. A Classification of Two-dimensional Endo-commutative Algebras over F_2. https://arxiv.org/abs/2211.04015

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