A radical splitting theorem for bernstein algebras

Abstract

We introduce the notion of radical in Bernstein algebras and prove a splitting theorem, that is an analog of a well-known statement in classical varieties of algebras. Note that in this situation Bernstein algebras are more similar to solvable Lie and Malcev algebras (see [4], [6]) than to associative, Jordan or Binary Lie ones.Throughout the paper all algebras and vector spaces are finite dimensional over an algebraically closed field k of characteristic 0.