Primary Decomposition of Powers of the Prime Ideal of a Numerical Semigroup Ring

Abstract

Let R=k[tn1,…,tns]=k[x1,…,xs]/P$R=k[t^{n_{1}},\\ldots ,t^{n_{s}}]=k[x_{1},\\ldots ,x_{s}]/P$ be a numerical semigroup ring and let P(n) = PnRP ∩ R be the symbolic power of P and Rs(P) = ⊕i≥\u20090P(n)tn the symbolic Rees ring of P. It is hard to determine symbolic powers of P; there are even non-Noetherian symbolic Rees rings for 3-generated semigroups. We determine the primary decomposition of powers of P for some classes of 3-generated numerical semigroups.