and cross-section g g G ¬ t. w x If p is prime, a p-valued field 8, p. 7 is a valued field, of characteristic zero, in which p has minimal positive value and whose residue field has p Ž . elements. A p-valued field F, ̈ is p-adically closed just in case no algebraic extension F9 of F with valuation ̈ 9 extending ̈ is p-valued. The Ž . class of p-adically closed fields is to Q , ̈ as the class of re...

We discuss the role of additive polynomials and p-polynomials in the theory of valued fields of positive characteristic and in their model theory. We outline the basic properties of rings of additive polynomials and discuss properties of valued fields of positive characteristic as modules over such rings. We prove the existence of Frobenius-closed bases of algebraic function fields F |K in one ...