Sur les algèbres de bernstein qui sont des T-algèbres

Power-associative algebras that are train algebras

“…Assume A is Bernstein of order 1. Since, by hypothesis, A is also a train algebra, it follows from [22] or [32] that A satisfies an equation of the…”

Bernstein algebras that are algebraic and the Kurosh problem

“…Another kind of non-associative algebras arising in the symbolism of genetics are the so-called train algebras, which were introduced by Etherington [19,20]. The class of Bern-stein algebras which are train algebras were studied by several authors (see, for instance, [21,39,45]), but mostly restricted to the finite-dimensional context.…”

On Bernstein algebras which are train algebras

“…As follows from a result of Outtara [9], the rank polynomial of a Bernstein train algebra is uniquely determined by its degree. This result admits an interpretation as a "stationarity principle" which is different from (1), and this in turn enables us to solve the differential equation for overlapping generations in the time-continuous model (for K = IR) in closed form.…”

“…In particular, for r k 3 let Theorem 2.1 (Ouattara [9]). Let A be a Bernstein train algebra, and the degree of its rank equation equal to r^3 .…”

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The class of non-associative algebras over a field of characteristic zero named in the title is studied using a result of Ouattara [9]. As an application, the differential equation for overlapping generations in the timecontinuous model is solved.

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