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

TL;DR

This paper introduces and studies new classes of Jordan algebras called RJ- and BJ-algebras, extending previous work on Rickart and Baer Jordan algebras, with criteria and properties explored.

Contribution

It defines RJ- and BJ-algebras, provides criteria for BJ-algebras, and proves finite-dimensional Jordan algebras without nilpotent elements with square roots are BJ-algebras.

Findings

Criteria established for BJ-algebras

Finite-dimensional Jordan algebras without nilpotent elements with square roots are BJ-algebras

Extended the class of Jordan algebras beyond Rickart and Baer types

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.