| 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  [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |
| 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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