When the associated graded ring of a semigroup ring is Complete Intersection

Abstract

Let (R,m) be the semigroup ring associated to a numerical semigroup S. In this paper we study the property of its associated graded ring grm(R) to be Complete Intersection. In particular, we introduce and characterize β-rectangular and γ-rectangular Apéry sets, which will be the fundamental concepts of the paper and will provide, respectively, a sufficient condition and a characterization for grm(R) to be Complete Intersection. Then we use these notions to give four equivalent conditions for grm(R) in order to be Complete Intersection.