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 gr m (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 gr m (R) to be Complete Intersection. Then we use these notions to give four equivalent conditions for gr m (R) in order to be Complete Intersection. MSC: 13A30; 13H10.

On the Apéry sets of monomial curves

“…By completely different methods it is proven in [19] that S is in fact complete intersection. Also, following the notation in [11], we have that Ap(S) is β-rectangular and then G(S) is complete intersection by [11, Corollary 2.10 and Theorem 3.6].…”