关键词: 赋值, 有理非离散, 超越形式级数, &phi, -次数

Abstract:

In this paper, we study the valuations of rational nondiscrete type. Let K be a 2-dimensional purely transcendental field extension of k. By defining the φ-degree of a monomial when φ is a formal series satisfying some given conditions, we show that every k-valuation of K can be defined by a transcendental formal series.

Key words: valuation, rational nondiscrete, transcendental formal series, φ-degree