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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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2019
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| Онлайн доступ: | 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 |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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| ISSN: | 1726-3255 |