Anton CEDILNIK

Classification of three-dimensional isopotent algebras

Anahtar Kelimeler:

Non-associative algebra, multiplication table, classification, isopotent, excess, three-dimensional, zeropotent, isoproduct

Classification of three-dimensional isopotent algebras

In the article, we perform a classification of algebras with dimensions $\leq$ 3 and with the property that each element is colinear with its square. The classification is complete up to properties of the ground field.

Keywords:

Non-associative algebra, multiplication table, classification, isopotent, excess, three-dimensional, zeropotent, isoproduct,

PDF

___

A. Cedilnik, Subassociative algebras, Acta Math. Univ. Comenian., 66(2) (1997), 229-241.
A. Cedilnik and M. Jerman , Classification of three-dimensional zeropotent algebras, Int. Electron. J. Algebra, 27 (2020), 127-146.
R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and its Applications, 20, Cambridge University Press, Cambridge, 1997.