Forms in Odd Degree Extensions and Self-Dual Normal Bases

Abstract

Introduction. Let K be a field. Springer has proved that an ani-sotropic quadratic form over K is also anisotropic over any odd degree extension of K (see [31], [14]). If the characteristic of K is not 2, this implies that two nonsingular quadratic forms that become isomorphic over an extension of odd degree of K are already isomorphic over K