A proof is given for the Ruled Residue Conjecture, which asserts that if v is a valuation of a simple transcendental field extension Ko(x) and vo is the restriction of v to Ko, then the residue field… Expand

We originally set out to determine if the converse to this theorem is valid; and we show in §2 that it is not. Proceeding from this point, we were led to a consideration of the following statements:… Expand

A quadratic form Q is called a special Pfister neighbor if Q is similar to a form of the shape P0 ⊥ aP1, where P0 is Pfister, a ∈ k*, and P1 is a nonzero subform of P0. The Pfister form P0 ⊥ aP0,… Expand