In this paper, we present a characterization for the defect of a simple algebraic extension of rank one valued fields using the key polynomials that define the valuation. As a particular example, this gives the classification of defect extensions of degree as dependent or independent presented by Kuhlmann.

中文翻译：

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一阶值域扩展缺陷的表征

在本文中，我们使用定义估值的关键多项式来描述一级值域的简单代数扩展的缺陷。作为一个特定的例子，这给出了缺陷扩展程度的分类库尔曼提出的从属或独立。