{"paper":{"title":"Derivations and differential operators on rings and fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Gergely Kiss, Mikl\\'os Laczkovich","submitted_at":"2018-03-02T19:50:44Z","abstract_excerpt":"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 d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01025","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}