Outer fractions in quadratic Jordan algebras

Using new techniques of Zel'manov, 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 imbedding in such an algebra of fractions. The details of the actual imbedding will appear in a subsequent paper.

J. Bowling < kmm4m@virginia.edu >

K. McCrimmon < jdb5e@yahoo.com >