Reference : Derivations and differential operators on rings and fields |
Scientific journals : Article | |||
Physical, chemical, mathematical & earth Sciences : Mathematics | |||
http://hdl.handle.net/10993/35285 | |||
Derivations and differential operators on rings and fields | |
English | |
Kiss, Gergely ![]() | |
Mar-2018 | |
Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Computatorica | |
Tankönyvkiadó | |
Yes | |
International | |
0138-9491 | |
Budapest | |
Hungary | |
[en] derivations of any order ; differential operators | |
[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. | |
Researchers ; Professionals ; Students | |
http://hdl.handle.net/10993/35285 | |
https://arxiv.org/pdf/1803.01025.pdf |
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