The index of a numerical semigroup ring

Let R=k[∣ta,tb,tc∣] be a complete intersection numerical semigroup ring over an infinite field k, where a,b,c∈N. The generalized Loewy length, which is Auslander’s index in this case, is computed in terms of the minimal generators of the semigroup: a,b and c. Examples provided show that the left hand side of Ding’s inequality mult(R)−index(R)−codim(R)+1≥0 can be made arbitrarily large for rings R with edim(R)=3. The index of a complete intersection numerical semigroup ring with embedding dimension greater than three is also computed.