Communications of the
Korean Mathematical Society CKMS

We provide a characterization of the emph{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