On Ideals of Submonoids of Power Monoids

Abstract

Let (Formula presented.) be a numerical monoid, while a (Formula presented.) -monoid S is a monoid generated by a finite number of finite non-empty subsets of (Formula presented.). 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 (Formula presented.) -monoids. These are the key to studying some factorization properties of (Formula presented.) -monoids and some additive properties of sumsets. This approach links computational commutative algebra with additive number theory.