×

zbMATH — the first resource for mathematics

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)

MSC:
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
PDF BibTeX XML Cite
Full Text: DOI