Robert W. Fitzgerald
Small extensions of Witt rings

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.