A RADICAL SPLITTING THEOREM FOR BERNSTEIN ALGEBRAS

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