Outer fractions in quadratic Jordan algebras

Using new techniques of Zelmanov, C. Martinez improved on work of Jacobson, McCrimmon, and Parvathi to give a necessary and sufficient Ore-type condition for an arbitrary linear Jordan algebra (with no 2- or 3-torsion) to have an algebra of fractions. In this paper we extend to quadratic algebras the concept of algebras of outer fractions with respect to an Ore monad, and describe necessary and sufficient Ore-type conditions for the embedding in such an algebra of fractions. The details of the actual embedding will appear in a subsequent paper. (C) 2007 Published by Elsevier Inc.