On the group of automorphisms of the semigroup ${\mathbf{B}}_{\mathbb{Z}}^{\mathcal{F}}$ with the family $\mathcal{F}$ of inductive nonempty subsets of $\omega$

Abstract

We study automorphisms of the semigroup ${\mathbf{B}}_Z^{\mathcal{F}}$ with the family $\mathcal{F}$ of inductive nonempty subsets of $\omega$ and prove that the group $\mathbf{Aut}({\mathbf{B}}_{\mathbb{Z}}^{\mathcal{F}})$ of automorphisms of the semigroup ${\mathbf{B}}_Z^{\mathcal{F}}$ is isomorphic to the additive group integers.

13 pages. 1 figure