Order relation in jb-algebras

摘要

In 4 we prove that the relation #x2264; defined byx #x2264; yif and only ifxy = x2, x2y - xy2= x3is an order relation for a class of Jordan rings. By a result of L. Bunce 3 it is easy to prove that this relation is also a partial order for JB-algebras. Then the aim of this paper is to compare this order relation with the usual order for JB-algebras and to obtain a characterization of a hyperatomic finite dimensional JB-algebra.