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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.

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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}
}

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19 pages