Derivations and differential operators on rings and fields
| Autor: | Kiss, Gergely, Laczkovich, Miklós |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $R$ be an integral domain of characteristic zero. We prove that a function $D\colon R\to R$ 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 $F\subset R$, there is a differential operator $D$ of degree $n$ such that $f=D$ on $F$. We also prove that if $d_1, \dots, d_n$ are nonzero derivations on $R$, then $d_1 \circ \ldots \circ d_n$ is a derivation of exact order $n$. Comment: 12 pages |
| Databáze: | arXiv |
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