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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