Local Lesieur–Croisot theory of Jordan algebras

In this paper we study Jordan algebras having nonzero local algebras that satisfy the property of being Lesieur–Croisot (i.e., being orders in nondegenerate Jordan algebras of finite capacity). We will prove that the set of the elements of a nondegenerate Jordan algebra at which the local algebra is Lesieur–Croisot is an ideal.