A Classification of Two-dimensional Endo-commutative Algebras over F_2
Rings and Algebras
2022-11-09 v1
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.
Keywords
Cite
@article{arxiv.2211.04015,
title = {A Classification of Two-dimensional Endo-commutative Algebras over F_2},
author = {Sin-Ei Takahasi and Kiyoshi Shirayanagi and Makoto Tsukada},
journal= {arXiv preprint arXiv:2211.04015},
year = {2022}
}
Comments
19 pages