AI 中文总结
本文证明了2021年Baeth等人提出的双UF正猜想，即原型半环N₀是唯一满足加法与非零乘法幺半群均为阶乘的正半环。
AI 中文摘要
包含1且为非负实数锥的子半环S称为正半环。2021年Baeth、Chapman和Gotti提出的双UF正猜想指出，原型半环N₀是唯一满足加法幺半群(S,+)和非零乘法幺半群(S^•,·)（其中S^•=S\{0}）均为阶乘的正半环。本文证明了该猜想成立。
英文摘要
A subsemiring $S$ of the nonnegative cone of the real line containing $1$ is called a positive semiring. The Bi-UF Positive Conjecture, posed by Baeth, Chapman, and Gotti in 2021, states that the prototypical semiring $\mathbb{N}_0$ is the only positive semiring whose additive monoid $(S,+)$ and nonzero multiplicative monoid $(S^\bullet,\cdot)$, where $S^\bullet=S\setminus\{0\}$, are both factorial. In this paper, we prove their conjecture.
