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
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