Polynomial identities of bicommutative algebras, Lie and Jordan elements

A. S. Dzhumadil'daev; N. A. Ismailov

Polynomial identities of bicommutative algebras, Lie and Jordan elements

Rings and Algebras 2017-11-15 v1

Authors: A. S. Dzhumadil'daev , N. A. Ismailov

Abstract

An algebra with identities $a(bc)=b(ac),$ $(ab)c=(ac)b$ is called bicommutative. We construct list of identities satisfied by commutator and anti-commutator products in a free bicommutative algebra. We give criterions for elements of a free bicommutative algebra to be Lie or Jordan.

Keywords

bicommutative algebras polynomial identities lie elements jordan elements commutator anti-commutator

Cite

@article{arxiv.1711.04300,
  title  = {Polynomial identities of bicommutative algebras, Lie and Jordan elements},
  author = {A. S. Dzhumadil'daev and N. A. Ismailov},
  journal= {arXiv preprint arXiv:1711.04300},
  year   = {2017}
}

Comments

14 pages

Related papers

View all related →