On the semigroup of injective monoid endomorphisms of the monoid ${\mathbf{B}}_{\omega }^{{\mathcal{F}}^3}$ with a three element family ${\mathcal{F}}^3$ of inductive nonempty subsets of $\omega$

Abstract

We describe injective monoid endomorphisms of the semigroup ${\mathbf{B}}_{\omega }^{{\mathcal{F}}^3}$ with a three element family ${\mathcal{F}}^3$ of inductive nonempty subsets of $\omega$. Also, we show that the monoid ${\mathbf{End}}_{\ast }^1({\mathbf{B}}_{\omega }^{\mathcal{F}})$ of all injective endomorphisms of the semigroup ${\mathbf{B}}_{\omega }^{{\mathcal{F}}^3}$ is isomorphic to the multiplicative semigroup of positive integers.

14 pages. arXiv ad14min note: substantial text overlap with arXiv:2307.15481, arXiv:2402.12386