Pfister's subform theorem for reduced special groups. (Q1434760)

Pfister's Subform Theorem says that if \(K\) is a field of characteristic different from 2 and \(\phi, \psi\) are quadratic forms over \(K\) with \(\psi\) anisotropic, then \(\phi\) is a subform of \(\psi\) if and only if the polynomial \(\phi(x)\) is represented in \(K(x)\) by the form \(\psi\otimes K(x)\) [\textit{M. Knebusch} and \textit{W. Scharlau}, Algebraic theory of quadratic forms. Generic methods and Pfister forms. DMV Seminar, 1. Boston: Birkhäuser Verlag (1980; Zbl 0439.10011)]. The aim of the paper is to formulate and prove this theorem in the setting of reduced special groups (in the meaning of \textit{M. A. Dickmann} and \textit{F. Miraglia} [Special groups. Boolean-theoretic methods in the theory of quadratic forms, Mem. Am. Math. Soc. 689 (2000; Zbl 1052.11027)]). In the proof the author uses Marshall's classification theorem for finite spaces of orderings and Pfister's Subform Theorem for Pythagorean fields.