On Ideals of Submonoids of Power Monoids

Let S be a numerical monoid, while a Pfin(S)-monoid S is a monoid generated by a finite number of finite non-empty subsets of S. That is, S is a non-cancellative commutative monoid obtained from the sumset of finite non-negative integer sets. This work provides an algorithm for computing the ideals associated with some Pfin(S)-monoids. These are the key to studying some factorization properties of Pfin(S)-monoids and some additive properties of sumsets. This approach links computational commutative algebra with additive number theory.