A Complete classification of two-dimensional endo-commutative algebras over an arbitrary field
Rings and Algebras
2024-07-09 v3
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 -dimensional algebras over any basic field.
Keywords
Cite
@article{arxiv.2304.00491,
title = {A Complete classification of two-dimensional endo-commutative algebras over an arbitrary field},
author = {D. Asrorov and U. Bekbaev and I. Rakhimov},
journal= {arXiv preprint arXiv:2304.00491},
year = {2024}
}