Let J be a Jordan algebra with 1. A subalgebra B of J is said to be full if 1 ∈ B and for any b in B with b invertible in J, b-1 ∈ B. We prove that if J is nondegenerate then any full subalgebra of J generated by two elements is special. It follows that any rational identity in two indeterminated satisfied in all special Jordan algebras is also satisfied in all nondegenerate Jordan algebras.
@article{urn:eudml:doc:39894,
title = {Sur une conjecture de Jacobson.},
journal = {Extracta Mathematicae},
volume = {5},
year = {1990},
pages = {141-143},
mrnumber = {MR1125686},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39894}
}
Essannouni, Hassane; Kaidi, Amine. Sur une conjecture de Jacobson.. Extracta Mathematicae, Tome 5 (1990) pp. 141-143. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39894/