Bernstein algebras were introduced by P. Holgate in [1] to deal with the problem of populations which are in equilibrium after the second generation. In [3] we work with Weak Bernstein Jordan algebras, i.e. a class of commutative algebras with idempotent element and defined by relations. In [3, section 4] we prove that if A= Ke ⊕ U ⊕ V is the Pierce decomposition of A relative to the idempotent e, then the situations U3 = {0} and U2(UV) = {0} are independents of the different Pierce decompositions of A, then they are invariants of A. We say that A is orthogonal if U3 = {0} and quasiorthogonal if U2(UV) = {0}. The orthogonality case was treated in [2].
In this paper we prove that every Bernstein-Jordan algebra of dimension less than 11 is quasi-orthogonal. Moreover we prove that there exists only one non quasi-orthogonal Bernstein-Jordan algebra of dimension 11.
@article{1562,
title = {On Quasi orthogonal Bernstein Jordan algebras},
journal = {CUBO, A Mathematical Journal},
year = {1992},
language = {en},
url = {http://dml.mathdoc.fr/item/1562}
}
Fuenzalida, Ana; Labra, Alicia; Mallol, Cristian. On Quasi orthogonal Bernstein Jordan algebras. CUBO, A Mathematical Journal, (1992), 6 p. http://gdmltest.u-ga.fr/item/1562/