论文标题
缺陷公式
The defect formula
论文作者
论文摘要
在本文中，我们介绍了一个简单代数延伸的缺陷的表征。这种表征概括了Henselian病例的已知结果，即缺陷是相对限量增强度相对程度的乘积。这里使用的主要工具是与多项式环上的估值相关的分级代数。令$ \ kh $为有价值的字段$ k $的henselization。本文证明的另一个相关结果是，对于$ \ khx $上的每个估值$ \ muh $，$ \ kx $上的限制$μ$，相应的映射$ \ MATHCALg_μ\ hk \ Mathcal g_ {\ mathcal g _ {\ muh} g _ {\ muh} $ geralgebras的级别是同胞的。
In this paper we present a characterization for the defect of a simple algebraic extensions of valued fields. This characterization generalizes the known result for the henselian case, namely that the defect is the product of the relative degrees of limit augmentations. The main tool used here is the graded algebra associated to a valuation on a polynomial ring. Let $\kh$ be a henselization of a valued field $K$. Another relevant result proved in this paper is that for every valuation $\muh$ on $\khx$, with restriction $μ$ on $\kx$, the corresponding map $\mathcal G_μ\hk\mathcal G_{\muh}$ of graded algebras is an isomorphism.
