On differential operators of numerical semigroup rings

2011/09/28 by Valentina Barucci, Ralf Fröberg, Barucci, Valentina +1
Decision Sciences · Mathematics · #13AXX #13N10 #13N15 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #Scheduling and Timetabling Solutions #math.AC #msc:13AXX #msc:13N10 #msc:13N15

paper · pdf · doi:10.48550/arxiv.1109.6118

13 pages

arxiv created 2011/09/28 · openalex publication_date 2011/09/28 · arxiv updated 2011/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If S=<d₁,...,d_ν> is a numerical semigroup, we call the ring \C[S]=\C[t^d₁,...,t^d_ν] 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).

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