Jordan counterparts of Rickart and Baer $*$-algebras, II

Abstract

We introduce and investigate new classes of Jordan algebras which are close to but wider than Rickart and Baer Jordan algebras considered in our previous paper. Such Jordan algebras are called RJ- and BJ-algebras respectively. Criterions are given for a Jordan algebra to be a BJ-algebra. Also, it is proved that every finite dimensional Jordan algebra without nilpotent elements, which have square roots, is a BJ-algebra.