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On Derivations Induced by p-Adic Fields

Published online by Cambridge University Press:  20 November 2018

N. Heerema  and
T. Morrison
N. Heerema
Affiliation:
Florida State University, Tallahassee, Florida
T. Morrison
Affiliation:
Talledega College, Talledega, Alabama
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This paper is concerned with a question which occurs in [6, p. 346] and uses the notation of that article. Thus K ⊃ K0 are p-adic fields (p ≠ 2) with residue fields k ⊃ k0 and having respective rings of integers R ⊃ R0, G0 = G0(K/K0) is the group of inertial automorphisms of K over K0,I(K/K0) is the R module of integral derivations on K over K0 and Ī(K/K0) is the k space of derivations on k induced by I(K/K0). The question here dealt with is the following. Given fields k ⊃ k0 of characteristic p(≠0, 2) with k/k0 finitely generated, which subspaces of the k space, Der(k/k0), of derivations on k over k0 have the form Ī(K/K0) for some pair of p-adic fields K ⊃ K0 having k ⊃ k0 as residue fields. We note the following connection between Ī(K/K0) and G0(K/K0).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 4 , 01 August 1981 , pp. 840 - 856
Copyright
Copyright © Canadian Mathematical Society 1981

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