3 problems

Bi-UFS Positive Conjecture. A positive semidomain $S$ is a bi-UFS if and only if

Let $S$ be an additively reduced and additively atomic semidomain, and let $cmathcal{A}_{+}(S)$ denote the set of additive atoms of $S$ and $S^{\times}$ its multiplicative unit gro…

Let $S$ be a positive semidomain. It is a bi-LFS if both $(S,+)$ and $S^\bullet$ are length-factorial monoids (LFMs), and a bi-UFS if both $(S,+)$ and $S^\bullet$ are unique-factor…