{"paper":{"title":"On differential operators of numerical semigroup rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ralf Fr\\\"oberg, Valentina Barucci","submitted_at":"2011-09-28T08:03:33Z","abstract_excerpt":"If $S=<d_1,...,d_\\nu>$ is a numerical semigroup, we call the ring $\\C[S]=\\C[t^{d_1},...,t^{d_\\nu}]$ the semigroup ring of $S$. We study the ring of differential operators on $\\C[S]$, and its associated graded in the filtration induced by the order of the differential operators. We find that these are easy to describe in case $S$ is a so called Arf semigroup. If $I$ is an ideal in $\\C[S]$ that is generated by monomials, we also give some results on $\\der(I,I)$ (the set of derivations which map $I$ into $I$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6118","kind":"arxiv","version":1},"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"}