Article (Scientific journals)
Derivations and differential operators on rings and fields
Kiss, Gergely
2018In Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Computatorica
Peer reviewed
 

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Keywords :
derivations of any order; differential operators
Abstract :
[en] Let R be an integral domain of characteristic zero. We prove that a function D : R → R is a derivation of order n if and only if D belongs to the closure of the set of differential operators of degree n in the product topology of R^R, where the image space is endowed with the discrete topology. In other words, f is a derivation of order n if and only if, for every finite set F ⊂ R, there is a differential operator D of degree n such that f = D on F. We also prove that if d1, . . . , dn are nonzero derivations on R, then d1 ◦ . . . ◦ dn is a derivation of exact order n.
Disciplines :
Mathematics
Author, co-author :
Kiss, Gergely ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Derivations and differential operators on rings and fields
Publication date :
March 2018
Journal title :
Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Computatorica
ISSN :
0138-9491
Publisher :
Tankönyvkiadó, Budapest, Hungary
Peer reviewed :
Peer reviewed
Available on ORBilu :
since 19 March 2018

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