A CHARACTERIZATION OF FINITE FACTORIZATION POSITIVE MONOIDS

We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the fi-nite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.