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Chapter VI Galois Theory of differential Fields

Elsevier B.V.
Publication Date
DOI: 10.1016/s0079-8169(08)62637-9


Throughout this chapter denotes a fixed universal differential field of characteristic 0 with field of constants . The set of derivation operators of , the set of derivative operators of , and the set of derivative operators of of order less than or equal to s are denoted by Δ,Θ and Δ(s), re-spectively; the elements of Δ are denoted by σ 1…σ m. Every differential field considered is tacitly assumed to be a differential subfield of . and always denote differential fields over which is universal.

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