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.

Notes

^*Supported by the Ministry of Education and Science of Spain, Directión General de Investigación Científica y Enseñanza Superior

Additional information

Notes on contributors

A. Grishkov

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