Moussa Ouattara

Sur les algèbres de bernstein qui sont des T-algèbres☆

Abstract In this note we show that for finite-dimensional Bernstein algebras over a field of characteristic different from 2: 1. (1) The principal nilpotency of an element implies its strong nilpotency. 2. (2) If Ker(ω) is a nil algebra, then it is a train algebra. 3. (3) Every train algebra of dimension n ⩽ 5 is special train algebra, and that is a best possible result.

Sur les algèbres de Bernstein d'ordre 2

Abstract We show that the duplicate of an n th order Bernstein algebra is a Bernstein algebra of order n +1, and we characterize the set of generalized idempotents in such an algebra. We also characterize those Bernstein algebra of order 2 which are Jordan or are power associative. The results are quite different from what is true for Bernstein algebras of order 1.

Sur une classe d'algèbres à puissances associatives

Abstract Many papers in connection with power associativity in genetic algebras show a class of commutative power-associative algebras which are one-dimensional modulo their maximal nil ideals. In this paper we study power-associative algebras with principal and absolutely primitive idempotent and the Peirce decomposition A = A 1 ⊕ A 1 2 ⊕ A 0 of which either A 1 is isomorphic to the ground field of A 0 = 0. In the first case, this class of algebras, which we call power-associative B - algebras , coincide with the class of Berstein algebras of order n ( n ⩾ 0) which are power-associative. Every power-associative B -algebra is a train algebra, and when it is a Jordan B -algebra, it is special train algebra. In the other case, we refer to power-associative algebras of type II . These algebras are also train algebras.

Algèbres génétiques dimensionnellement nilpotentes

Abstract 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 Osborns results about Jordan algebras.