O. T. Izhboldin

On the nonexcellence of field extensions $F(\pi)/F$

Abstract

For any $n\ge3$ we construct a field $F$ and $n$-fold Pfister form $\phi$ such that the field extension $F(\phi)/F$ is not excellent. We prove that $F(\phi)/F$ is universally excellent if and only if $\phi$ is a Pfister neighbor of dimension $\le4$.

Keywords and Prases: Quadratic forms, Pfister form, excellent field extension.

1991 Mathematics Subject Classification: Primary 11E04; Secondary 11E81, 12F20