On ideals of affine semigroups and affine semigroups with maximal embedding dimension

Let S⊆ Nᵖ be a semigroup, any P⊆ S is an ideal of S if P+S⊆ P, and an $I(S)$-semigroup is the affine semigroup P∪ \0\, with P an ideal of S. We characterise the $I(S)$-semigroups and the ones that also are C-semigroups. Moreover, some algorithms are provided to compute all the $I(S)$-semigroups satisfying some properties. From a family of ideals of S, we introduce the affine semigroups with maximal embedding dimension, characterising them and describing some families.