On a class of quadratic algebras

Abstract

We shall denote this class by e. The commutative algebras in e are the well-known central simple Jordan algebras of degree two. In [3] an example is given (over F containing v-I of a 7-dimensional algebra in e which is not commutative. We shall denote by C' the class of all algebras in C which are not commutative. In this note we show that, in the presence of the other conditions on the algebras in C, identity (1) may be replaced by