Polynomial identities of bicommutative algebras, Lie and Jordan elements

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.

14 pages

References in corpus (2)

• Noetherianity and Specht problem for varieties of bicommutative algebras
• Lie elements in pre-Lie algebras, trees and cohomology operations