AI 中文总结
该研究刻画了带有四元归纳非空子集族ℱ⁴的半群B_ω^ℱ⁴的单态射，证明其每个单幺半群态射为恒等变换，还刻画了所有单态射
AI 中文摘要
我们刻画了带有ω的四元归纳非空子集族ℱ⁴的半群B_ω^ℱ⁴的单态射，特别证明该半群的每个单幺半群态射都是恒等变换，还刻画了该半群的所有（未必是幺半群的）单态射
英文摘要
We describe injective endomorphisms of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}^4}$ with a four-element family $\mathscr{F}^4$ of inductive non-empty subsets of $ω$. In particular we proved that every injective monoid endomorphism of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}^4}$ is the identity transformation. Also we describe all (not necessary monoid) injective endomorphism of $\boldsymbol{B}_ω^{\mathscr{F}^4}$.
Comments12 pages
