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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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Інститут прикладної математики і механіки НАН України
2019
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/188431 |
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irk-123456789-1884312023-03-02T01:27:09Z Automorphism groups of superextensions of finite monogenic semigroups Banakh, T.O. Gavrylkiv, V.M. 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. 2019 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/188431 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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English |
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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. |
| format |
Article |
| author |
Banakh, T.O. Gavrylkiv, V.M. |
| spellingShingle |
Banakh, T.O. Gavrylkiv, V.M. Automorphism groups of superextensions of finite monogenic semigroups Algebra and Discrete Mathematics |
| author_facet |
Banakh, T.O. Gavrylkiv, V.M. |
| author_sort |
Banakh, T.O. |
| title |
Automorphism groups of superextensions of finite monogenic semigroups |
| title_short |
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_sort |
automorphism groups of superextensions of finite monogenic semigroups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2019 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188431 |
| 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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT banakhto automorphismgroupsofsuperextensionsoffinitemonogenicsemigroups AT gavrylkivvm automorphismgroupsofsuperextensionsoffinitemonogenicsemigroups |
| first_indexed |
2023-10-18T23:08:21Z |
| last_indexed |
2023-10-18T23:08:21Z |
| _version_ |
1796157348147888128 |