The Koszulness of numerical semigroup rings of minimal multiplicity

Abstract

Let R = k [H] be a numerical semigroup ring over a field k and grm (R) is the associated graded ring of R. In this paper, we show that grm (R) is a Cohen-Macaulay ring, provided H has minimal multiplicity. As a consequence, we conclude that the numerical semigroup ring R = k [H] of minimal multiplicity is a Koszul ring, i.e., the residue field k has a grm (R) – linear free resolution.