Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A CHARACTERIZATION OF FINITE FACTORIZATION POSITIVE MONOIDS

  • Polo, Harold (Mathematics Department University of Florida)
  • Received : 2021.08.07
  • Accepted : 2021.10.29
  • Published : 2022.07.31
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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

Acknowledgement

I am grateful to Felix Gotti for his guidance during the preparation of this paper, in particular, for many useful conversations that lead up to the discovery of Theorem 3.3. While working on the same, I was generously supported by the University of Florida Mathematics Department Fellowship and the CAM Summer Research Fellowship.

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