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

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 is...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-11
Main Authors: Sin-Ei Takahasi, Shirayanagi, Kiyoshi, Tsukada, Makoto
Format: Article
Language:English
Subjects:
Algebra
Classification
Commutativity
Isomorphism
Mathematical tables
Multiplication
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422