English

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 22-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}
}