Structure des algèbres de Bernstein

Power-associative algebras that are train algebras

“…In particular, B(1, 1)-algebras are just the well-known Bernstein algebras [19,33]. First of all, we start by stating the following useful lemma.…”

On Bernstein algebras satisfying chain conditions II

“…As a special case, we derive that a commutative nilalgebra of nilindex 3 which is Noetherian or Artinian is finite-dimensional. In the final section, we intend to ameliorate and extend some results of Micali and Ouattara [19] to the Noetherian and Artinian cases. Various examples are presented along this work to serve as motivation and illustration for our results.…”

“…In this final section we shall proceed to revisit some results of Micali and Ouattara [19] in the aim to improve and generalize them to the Noetherian and Artinian situations. First, we start with the following result which was proved in [19,Lemmas 4.3 and 4.4] when the Bernstein algebra A was assumed to be finitely generated. Proof.…”

On Bernstein Algebras Satisfying Chain Conditions

“…We collect now some well-known results about these algebras (see, for instance, González and Martínez, 1994;Lyubich, 1992;Micali and Ouattara, 1995;Wörz-Buzekros, 1980). For every idempotent e of the Bernstein algebra A , the Peirce components multiply according to…”

“…In Costa and Guzzo (1993), the authors gave a Krull-Schmidt theorem for baric algebras satisfying chain conditions on ideals. In Micali and Ouattara (1995), it was considered in one result finitely generated Bernstein algebras with descending chain conditions. But as far as we know, Noetherian (Artinian) Bernstein algebras have not been studied systematically.…”