ABSTRACT KEY POLYNOMIALS AND COMPARISON THEOREMS WITH THE KEY POLYNOMIALS OF MAC LANE-VAQUIE

摘要

Let (K, v) be a valued field and K(x) a simple purely transcendental extension of K. In the nineteen thirties, in order to study the possible extensions of v to K(x), S. Mac Lane considered the special case when v is discrete of rank 1, and introduced the notion of key polynomials. M. Vaquie extended this definition to the case of arbitrary valuations. In this paper we give a new definition of key polynomials (which we call abstract key polynomials) and study the relationship between them and key polynomials of Mac Lane-Vaquie.