有理非离散型赋值(英文)

Valuations of rational nondiscrete type

研究了有理非离散型赋值.令K为k的2维纯超越域扩张.通过定义一个单项式的φ-次数,其中φ是满足给定条件的形式级数,得到K的每个k赋值都可以由一个超越形式级数来定义.

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.