Archiv der Mathematik ( IF 0.6 ) Pub Date : 2021-05-08 , DOI: 10.1007/s00013-021-01603-2 El Hassane Fliouet
Let K be a finitely generated extension of a field k of characteristic \(p\not =0\). In 1947, Dieudonné initiated the study of maximal separable intermediate fields. He gave in particular the form of an important subclass of maximal separable intermediate fields D characterized by the property \(K\subseteq k({D}^{p^{-\infty }})\), and which are called the distinguished subfields of K/k. In 1970, Kraft showed that the distinguished maximal separable subfields are precisely those over which K is of minimal degree. This paper grew out of an attempt to find a new characterization of distinguished subfields of K/k by means of new inseparability invariants.
中文翻译:
关于不可分领域扩展的不变量
令K为特征\(p \ not = 0 \)的场k的有限生成的扩展。1947年,Dieudonné开始研究最大可分离中间场。他特别给出了最大可分离中间字段D的一个重要子类的形式,该子类的特征是属性\(K \ subseteq k({D} ^ {p ^ {-\ infty}})\),这被称为K / k的子字段。1970年,卡夫(Kraft)表明,最大的可分离子场恰好是K最小程度的子场。本文源于试图找到K的显着子域的新特征的尝试/ k通过新的不可分不变性。