Structure des algèbres de Bernstein Original Research Article

The theory of Bernsteinʹs algebras is revisited. Many results concerning the structure of Bernstein algebras (ideals, nilpotency and so on) are stated. For Bernstein-Jordan algebras, we give a definitive formulation of the theorem which characterizes them. Finally, we emphasize the importance of the invariant L (this ideal doesnʹt depend on the Peirce decomposition of the algebra) in the study of the structure of Bernsteinʹs algebras.