Jordan counterparts of Rickart and Baer \(*\)-algebras, II

We introduce and investigate new classes of Jordan algebras which are close to but wider than Rickart and Baer Jordan algebras. Such Jordan algebras are called weak RJ- and weak BJ-algebras respectively. Criterions are given for a Jordan algebra to be a weak BJ-algebra. Also, it is proved that every finite dimensional Jordan algebra A, the degenerate radical of which does not have nilpotent elements with a square root in A and the quotient with respect to this radical of which has no nilpotent elements, is a weak BJ-algebra.