Abstract: | Abstract Let S be a numerical semigroup and let I be a relative ideal of S. Let S ? I denote the dual of I and let μ S (?) represent the size of a minimal generating set. We investigate the inequality μ S (I)μ S (S ? I) ≥ μ S (I + (S ? I)) under the assumption that S has multiplicity 8. We will show that if I is non-principal, then the strict inequality μ S (I)μ S (S ? I) > μ S (I + (S ? I)) always holds. |