论文标题
关于有价值的田地的常见扩展
On common extensions of valued fields
论文作者
论文摘要
给定一个字段$ k $的估值$ v $，向代数关闭的扩展$ \ bar {v} $和扩展名$ w $ to $ k（x）$。我们想研究$ \ bar {v} $和$ w $ to $ \ bar {k}（x）$的常见扩展。首先，我们在最小对概念与关键多项式概念之间提供了详细的联系。然后，我们证明，在$ w $是先验扩展的情况下，任何关键多项式的序列都允许最大元素，并且如果此序列不包含极限密钥多项式，那么最后一个键多项式的任何根，则描述一个常见的扩展。
Given a valuation $v$ on a field $K$, an extension $\bar{v}$ to an algebraic closure and an extension $w$ to $K(X)$. We want to study the common extensions of $\bar{v}$ and $w$ to $\bar{K}(X)$. First we give a detailed link between the minimal pairs notion and the key polynomials notion. Then we prove that in the case when $w$ is a transcendental extension, then any sequence of key polynomials admits a maximal element, and in case this sequence does not contain a limit key polynomial, then any root of the last key polynomial, describe a common extension.
