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.
Fitzgerald, Robert W. "Small Extensions of Witt Rings." (May 1999).