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Higher Derivations and Distinguished Subfields

Published online by Cambridge University Press:  20 November 2018

James K. Deveney  and
Nickolas Heerema
James K. Deveney
Affiliation:
Virginia Commonwealth University, Richmond, Virginia
Nickolas Heerema
Affiliation:
Florida State University, Tallahassee, Florida
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Let L be a finitely generated extension of a field K having characteristic p ≠ 0. A rank t higher derivation on L over K is a sequence

of additive maps of K into K such that

d0 is the identity map and dt(x) = 0, i > 0, x ∊ K. [6] contains the relevant background material on higher derivations. By Zorn's Lemma, there are maximal separable extensions of K in L. A maximal separable extension D of K in L is called distinguished if

Dieudonné [4] established that any finitely generated extension always has distinguished subfields. L has the same dimension over any distinguished subfield [5], and this dimension is called the order of inseparability of L/K. The least n such that K(LP)n is separable over K is called the inseparable exponent of L/K, inex(L/K).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 1 , 01 February 1988 , pp. 131 - 141
Copyright
Copyright © Canadian Mathematical Society 1988

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