On the semigroup of injective monoid endomor\-phisms of the monoid $\boldsymbol{B}_ω^{\mathscr{F}}$ with the two-elements family $\mathscr{F}$ of inductive nonempty subsets of $ω$
Олег Гутік, Inna Pozdniakova · arXiv (Cornell University) · 2023
We study injective endomorphisms of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}}$ with the two-elements family $\mathscr{F}$ of inductive nonempty subsets of $ω$. We describe the elements of the semigroup $\boldsymbol{End}^1_*(\boldsymbol{B}_ω^{\mathscr{F}})$ of all injective monoid endomorphisms of the monoid $\boldsymbol{B}_ω^{\mathscr{F}}$, and show that Green's relations $\mathscr{R}$, $\mathscr{L}$, $\mathscr{H}$, $\mathscr{D}$, and $\mathscr{J}$ on $\boldsymbol{End}^1_*(\boldsymbol{B}_ω^{\mathscr{F}})$ coincide with the relation of equality.