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The Order of Inseparability of Fields

Published online by Cambridge University Press:  20 November 2018

James K. Deveney  and
John N. Mordeson
James K. Deveney
Affiliation:
Virginia Commonwealth University, Richmond, Virginia
John N. Mordeson
Affiliation:
Creighton University, Omaha, Nebraska
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Let L be a finitely generated field extension of a field K of characteristic p ≠ 0. By Zorn's Lemma there exist maximal separable extensions of K in L and L is finite dimensional purely inseparable over any such field. If ps is the smallest of the dimensions of L over such maximal separable extensions of K in L, then s is Wiel's order of inseparability of L/K [11]. Dieudonné [2] also investigated maximal separable extensions D of K in L and established that there must be at least one D such that L ⊆ Kp–∞(D) (such fields are termed distinguished). Kraft [5] showed that the distinguished maximal separable subfields are precisely those over which L is of minimal degree. This concept of distinguished subfield has been the basis of a number of results on the structure of inseparable field extensions, for example see [1], [3], [5], and [6].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 3 , 01 June 1979 , pp. 655 - 662
Copyright
Copyright © Canadian Mathematical Society 1979

References

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