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

  • O.T. Izhboldin

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

For any n3n\ge3, we construct a field FF and an nn-fold Pfister form φ\varphi such that the field extension F(φ)/FF(\varphi)/F is not excellent. We prove that F(φ)/FF(\varphi)/F is universally excellent if and only if φ\varphi is a Pfister neighbor of dimension 4\le4.

Cite this article

O.T. Izhboldin, On the nonexcellence of field extensions F(π)/FF(\pi)/F. Doc. Math. 1 (1996), pp. 127–136

DOI 10.4171/DM/6