Abstract
In [ll, p. 4291, Jacobson proposed the problem of establishing a P.I. theory for Jordan rings. In particular he asks whether every simple P.I. Jordan algebra is either finite dimensional or gotten from a nondegenerate quadratic form. Jordan P.I. rings were then investigated by Smith and Rowen [15-17, and their bibliographies] among others. In this paper we investigate the structure of nondegenerate prime Jordan P.I. algebras with nonzero socle (see Section 2 for definitions). Using the classification of prime Jordan rings with nonzero socle established in a preceeding paper [13], we prove (in Section 2)
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