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.
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