A characterization of finite factorization positive monoids Commun. Korean Math. Soc. Published online May 12, 2022 Harold Polo University of Florida Abstract : We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite 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. Keywords : well-ordered set, co-well-ordered set, positive monoid, Puiseux monoid, semiring, positive semiring, finite factorization property, factorization theory MSC numbers : Primary: 20M13; Secondary: 16Y60, 06F05, 20M14 Full-Text :