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

• Date: 2023
• Main Authors: Gutik, O., Pozdniakova, I.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2023
• Subjects: bicyclic monoid; inverse semigroup; bicyclic extension; automorphism; group of automorphism; order-convex set; order isomorphism; Primary 20M18; Secondary 20F29; 20M10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2010
• Journal Title: Algebra and Discrete Mathematics

We study automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\) and prove that the group \(\mathbf{Aut}(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}})\) of automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{...