Hereditarily Finitely Generated Commutative Monoids

Numerical semigroups with embedding dimension three

“…P r o o f. As we pointed out in the Introduction, it is well known (see for instance [9]) that #Ap(S, n) = n for all n ∈ S \ {0}. Note that from the minimality of c 2 and c 3 , if…”

On morphisms of commutative monoids

“…, (a t , b t )} of σ with respect to on N p (see Chap. 6 of [6]). By using η, a canonical system of generators, we can compute for every element x, the minimum of [x] σ .…”

“…It can be easily shown that σ ⊆∼ M σ and that if (a, b) ∈∼ M σ , then there exists c ∈ F (X) such that (a + c, b + c) ∈ σ (the proof is the same as Lemma 1.3 of [6]). Hence one can define S can as…”

“…We refer the reader to [6] for further information. Let S be a set and + a binary operation over S. The pair (S, +) is a monoid if + satisfies the associative property and if there exists in S an identity element for + (denoted by 0).…”

“…Define NF η (x) = min([x] σ ); so xσy if and only if NF η (x) = NF η (y). If ρ and ρ are two subsets of N p × N p and we want to check whether ρ = ρ , it is only necessary to compute canonical systems of generators for ρ and ρ with respect to the same order and see if they are equal (see Algorithm 6.8 of [6]). …”