Automorphism groups of superextensions of finite monogenic semigroups
A family L of subsets of a set X is called linked if A ∩ B ≠ ∅ for any A,B ∈ L. A linked family M of subsets of X is maximal linked if M coincides with each linked family L on X that contains M. The superextension λ(X) of X consists of all maximal linked families on X. Any associative binary operat...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2019 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/188431 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Automorphism groups of superextensions of finite monogenic semigroups / T.O. Banakh, V.M. Gavrylkiv // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 2. — С. 165–190. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862750579122503680 |
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| author | Banakh, T.O. Gavrylkiv, V.M. |
| author_facet | Banakh, T.O. Gavrylkiv, V.M. |
| citation_txt | Automorphism groups of superextensions of finite monogenic semigroups / T.O. Banakh, V.M. Gavrylkiv // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 2. — С. 165–190. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | A family L of subsets of a set X is called linked if A ∩ B ≠ ∅ for any A,B ∈ L. A linked family M of subsets of X is maximal linked if M coincides with each linked family L on X that contains M. The superextension λ(X) of X consists of all maximal linked families on X. Any associative binary operation ∗ : X ×X → X can be extended to an associative binary operation ∗ : λ(X) × λ(X) → λ(X). In the paper we study automorphisms of the superextensions of finite monogenic semigroups and characteristic ideals in such semigroups. In particular, we describe the automorphism groups of the superextensions of finite monogenic semigroups of cardinality 6 5.
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| first_indexed | 2025-12-07T21:06:33Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-188431 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T21:06:33Z |
| publishDate | 2019 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Banakh, T.O. Gavrylkiv, V.M. 2023-03-01T15:28:51Z 2023-03-01T15:28:51Z 2019 Automorphism groups of superextensions of finite monogenic semigroups / T.O. Banakh, V.M. Gavrylkiv // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 2. — С. 165–190. — Бібліогр.: 24 назв. — англ. 1726-3255 2010 MSC: 20D45, 20M15, 20B25. https://nasplib.isofts.kiev.ua/handle/123456789/188431 A family L of subsets of a set X is called linked if A ∩ B ≠ ∅ for any A,B ∈ L. A linked family M of subsets of X is maximal linked if M coincides with each linked family L on X that contains M. The superextension λ(X) of X consists of all maximal linked families on X. Any associative binary operation ∗ : X ×X → X can be extended to an associative binary operation ∗ : λ(X) × λ(X) → λ(X). In the paper we study automorphisms of the superextensions of finite monogenic semigroups and characteristic ideals in such semigroups. In particular, we describe the automorphism groups of the superextensions of finite monogenic semigroups of cardinality 6 5. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Automorphism groups of superextensions of finite monogenic semigroups Article published earlier |
| spellingShingle | Automorphism groups of superextensions of finite monogenic semigroups Banakh, T.O. Gavrylkiv, V.M. |
| title | Automorphism groups of superextensions of finite monogenic semigroups |
| title_full | Automorphism groups of superextensions of finite monogenic semigroups |
| title_fullStr | Automorphism groups of superextensions of finite monogenic semigroups |
| title_full_unstemmed | Automorphism groups of superextensions of finite monogenic semigroups |
| title_short | Automorphism groups of superextensions of finite monogenic semigroups |
| title_sort | automorphism groups of superextensions of finite monogenic semigroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188431 |
| work_keys_str_mv | AT banakhto automorphismgroupsofsuperextensionsoffinitemonogenicsemigroups AT gavrylkivvm automorphismgroupsofsuperextensionsoffinitemonogenicsemigroups |