Small extensions of Witt rings

Robert W. Fitzgerald

Vol. 189 (1999), No. 1, 31–53

DOI: 10.2140/pjm.1999.189.31

Abstract

We consider certain Witt ring extensions S of a noetherian Witt ring R obtained by adding one new generator. The conditions on the new generator are those known to hold when R is the Witt ring of a field F, S is the Witt ring of a field K and K ∕ F is an odd degree extension. We show that if R is of elementary type then so is S.

Milestones

Received: 29 September 1997

Revised: 25 March 1998

Published: 1 May 1999