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arXiv · 2304.00491

A Complete classification of two-dimensional endo-commutative algebras over an arbitrary field

D. Asrorov·U. Bekbaev·I. Rakhimov
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Abstract

In the paper, we consider the class of so-called endo-commutative algebras. From the identity imposed to specify this class, one can easily see that the product in this class preserves the square of elements. We give a complete classification of this class, up to isomorphism, over any basic field in dimension two. This elementary and self-contained exposition uses the recent result of one of the authors on description of the category of all $2$-dimensional algebras over any basic field.

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D. Asrorov, U. Bekbaev, I. Rakhimov. 2023-04-02. A Complete classification of two-dimensional endo-commutative algebras over an arbitrary field. https://arxiv.org/abs/2304.00491

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