Abstract
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.
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Fliouet, E.H. On the invariants of inseparable field extensions. Arch. Math. 117, 155–164 (2021). https://doi.org/10.1007/s00013-021-01603-2
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DOI: https://doi.org/10.1007/s00013-021-01603-2