Automorphism groups of superextensions of finite monogenic semigroups
A family \(\mathcal L\) of subsets of a set \(X\) is called linked if \(A\cap B\ne\emptyset\) for any \(A,B\in\mathcal L\). A linked family \(\mathcal M\) of subsets of \(X\) is maximal linked if \(\mathcal M\) coincides with each linked family \(\mathcal L\) on \(X\) that contains \(\mathcal M\)....
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| Дата: | 2019 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2019
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1225 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | A family \(\mathcal L\) of subsets of a set \(X\) is called linked if \(A\cap B\ne\emptyset\) for any \(A,B\in\mathcal L\). A linked family \(\mathcal M\) of subsets of \(X\) is maximal linked if \(\mathcal M\) coincides with each linked family \(\mathcal L\) on \(X\) that contains \(\mathcal M\). The superextension \(\lambda(X)\) of \(X\) consists of all maximal linked families on \(X\). Any associative binary operation \(* : X\times X \to X\) can be extended to an associative binary operation \(*: \lambda(X)\times\lambda(X)\to\lambda(X)\). 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 \(\leq 5\). |
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