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Dérivations, et hautes dérivations, dans certains corps gauches de séries de Laurent. (Derivations, and higher derivations, in certain skew fields of Laurent series). (French) Zbl 0723.16019
Let k be a field of characteristic zero, \(F=k((Y))\) the local field of Laurent series in a variable Y, and \(\partial_ Y\) the usual derivation on F. The purpose of this paper is the complete description of k- derivations on the formal pseudo-differential operator skewfield \(K=F((X,\partial_ Y))\). An application of this result is given to study the structure of higher derivations in skewfields of characteristic zero.
Reviewer: R.Vidal (Aubière)

16W20 Automorphisms and endomorphisms
16S32 Rings of differential operators (associative algebraic aspects)
16K40 Infinite-dimensional and general division rings
16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras)
16S34 Group rings
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