Generic splitting fields of composition algebras

Abstract

Witt [7] proved that one can assign to each generalized quaternion algebra -' over a field K, a field F(sQI) containing K which splits S( and has the property: if F(a) splits a quaternion algebra 4 over K then either M is split over K or V is isomorphic to a. Amitsur [2] has generalized this result to obtain generic splitting fields for all central simple associative algebras of dimension greater than one over K (cf. Roquette [6]). In this paper we generalize the result of Witt in another direction, studying splitting fields of composition algebras of dimension greater than one over K of characteristic other than two. We assign to each such algebra ', a field F(e) containing K, prove that F(W) is an invariant under isomorphisms, and prove