It is shown that any split product of quatemion algebras with orthogonal involution is adjoint to a Pfister form. This settles the Pfister Factor Conjecture formulated by D.B. Shapiro. A more general problem on decomposability for algebras with involution is posed and solved in the case where the algebra is equivalent to a quatemion algebra.Let K be a field of characteristic different from 2. By a K -algebra with involution we mean a pair (A, a) of a central simple K -algebra A and a K -linear involution a : A ---* A. Involutions of this kind are either orthogonal or symplectic.A (regular) quadratic form
A recently found local-global principle for quadratic forms over function fields of curves over a complete discretely valued field is applied to the study of quadratic forms, sums of squares, and related field invariants.
In this article weakly isotropic quadratic forms over a (formally) real field are studied. Conditions on the field are given which imply that every weakly isotropic form over that field has a weakly isotropic subform of small dimension. Fields over which every quadratic form can be decomposed into an orthogonal sum of a strongly anisotropic form and a torsion form are characterized in different ways.
Given a central simple algebra with involution over an arbitrary field,
\'etale subalgebras contained in the space of symmetric elements are
investigated. The method emphasizes the similarities between the various types
of involutions and privileges a unified treatment for all characteristics
whenever possible. As a consequence a conceptual proof of a theorem of Rowen is
obtained, which asserts that every division algebra of exponent two and degree
eight contains a maximal subfield that is a triquadratic extension of the
centre
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