On the group of automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\)
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}}^{...
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| Дата: | 2023 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2023
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2010 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-20102023-06-19T09:27:54Z On the group of automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\) Gutik, O. Pozdniakova, I. bicyclic monoid, inverse semigroup, bicyclic extension, automorphism, group of automorphism, order-convex set, order isomorphism Primary 20M18; Secondary 20F29, 20M10 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 \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) is isomorphic to the additive group of integers. Lugansk National Taras Shevchenko University 2023-06-18 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2010 10.12958/adm2010 Algebra and Discrete Mathematics; Vol 35, No 1 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2010/pdf Copyright (c) 2023 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
bicyclic monoid inverse semigroup bicyclic extension automorphism group of automorphism order-convex set order isomorphism Primary 20M18; Secondary 20F29 20M10 |
| spellingShingle |
bicyclic monoid inverse semigroup bicyclic extension automorphism group of automorphism order-convex set order isomorphism Primary 20M18; Secondary 20F29 20M10 Gutik, O. Pozdniakova, I. On the group of automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\) |
| topic_facet |
bicyclic monoid inverse semigroup bicyclic extension automorphism group of automorphism order-convex set order isomorphism Primary 20M18; Secondary 20F29 20M10 |
| format |
Article |
| author |
Gutik, O. Pozdniakova, I. |
| author_facet |
Gutik, O. Pozdniakova, I. |
| author_sort |
Gutik, O. |
| title |
On the group of automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\) |
| title_short |
On the group of automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\) |
| title_full |
On the group of automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\) |
| title_fullStr |
On the group of automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\) |
| title_full_unstemmed |
On the group of automorphisms of the semigroup \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) with the family \(\mathscr{F}\) of inductive nonempty subsets of \(\omega\) |
| title_sort |
on the group of automorphisms of the semigroup \(\mathbf{b}_{\mathbb{z}}^{\mathscr{f}}\) with the family \(\mathscr{f}\) of inductive nonempty subsets of \(\omega\) |
| description |
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 \(\mathbf{B}_{\mathbb{Z}}^{\mathscr{F}}\) is isomorphic to the additive group of integers. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2023 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2010 |
| work_keys_str_mv |
AT gutiko onthegroupofautomorphismsofthesemigroupmathbfbmathbbzmathscrfwiththefamilymathscrfofinductivenonemptysubsetsofomega AT pozdniakovai onthegroupofautomorphismsofthesemigroupmathbfbmathbbzmathscrfwiththefamilymathscrfofinductivenonemptysubsetsofomega |
| first_indexed |
2024-04-12T06:26:46Z |
| last_indexed |
2024-04-12T06:26:46Z |
| _version_ |
1796109193371975680 |