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Algebra and Discrete Mathematics, 2019, том 27, выпуск 2, страницы 165–190
(Mi adm701)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
RESEARCH ARTICLE
Automorphism groups of superextensions of finite monogenic semigroups
Taras Banakhab, Volodymyr Gavrylkivc a Ivan Franko National University of Lviv Ukraine
b Jan Kochanowski University in Kielce, Poland
c Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
Аннотация:
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 $*\colon X\times X \to X$ can be extended to an associative binary operation $*\colon \lambda(X)\times\lambda(X)\to\lambda(X)$. 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 $\leq 5$.
Ключевые слова:
monogenic semigroup, maximal linked upfamily, superextension, automorphism group.
Поступила в редакцию: 05.08.2018 Исправленный вариант: 10.02.2019
Образец цитирования:
Taras Banakh, Volodymyr Gavrylkiv, “Automorphism groups of superextensions of finite monogenic semigroups”, Algebra Discrete Math., 27:2 (2019), 165–190
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm701 https://www.mathnet.ru/rus/adm/v27/i2/p165
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