Algèbres génétiques dimensionnellement nilpotentes

The structure of dimensionally nilpotent Lie algebras was studied by G. F. Leger and P. L. Manley for characteristic zero and by J. M. Osborn for characteristic p> 5. Moreover, J. M. Osborn studied dimensionally nilpotent commutative and noncommutative Jordan algebras. In this paper we give some results concerning Bernstein and genetic algebras which are dimensionally nilpotent in connection with Osbornʹs results about Jordan algebras.