C-Semigroups and Their Induced Order

Let C subset of N-p be an integer polyhedral cone. An affine semigroup S subset of C is a C-semigroup if |C\S| < + infinity. This structure has always been studied using a monomial order. The main issue is that the choice of these orders is arbitrary. In the present work, we choose the order given by the semigroup itself, which is a more natural order. This allows us to generalise some of the definitions and results known from numerical semigroup theory to C-semigroups.