Topological semigroups of matrix units

We prove that the semigroup of matrix units is stable. Compact, countably compact and pseudocompact topologies \(\tau\) on the infinite semigroup of matrix units \(B_\lambda\) such that \((B_\lambda,\tau)\) is a semitopological (inverse) semigroup are described. We prove the following properties of...

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Дата:2018
Автори: Gutik, Oleg V., Pavlyk, Kateryna P.
Формат: Стаття
Мова:English
Опубліковано: Lugansk National Taras Shevchenko University 2018
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Онлайн доступ:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/924
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-924
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spelling admjournalluguniveduua-article-9242018-03-21T06:47:49Z Topological semigroups of matrix units Gutik, Oleg V. Pavlyk, Kateryna P. semigroup of matrix units, semitopological semigroup, topological semigroup, topological inverse semigroup, \(H\)-closed semigroup, absolutely \(H\)-closed semigroup, algebraically \(h\)-closed semigroup, Bohr compactification 20M15, 20M18, 22A15, 54A10, 54C25, 54D25, 54D35, 54H10 We prove that the semigroup of matrix units is stable. Compact, countably compact and pseudocompact topologies \(\tau\) on the infinite semigroup of matrix units \(B_\lambda\) such that \((B_\lambda,\tau)\) is a semitopological (inverse) semigroup are described. We prove the following properties of an infinite topological semigroup of matrix units. On the infinite semigroup of matrix units there exists no semigroup pseudocompact topology. Any continuous homomorphism from the infinite topological semigroup of matrix units into a compact topological semigroup is annihilating. The semigroup of matrix units is algebraically \(h\)-closed in the class of topological inverse semigroups. Some \(H\)-closed minimal semigroup topologies on the infinite semigroup of matrix units are considered. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/924 Algebra and Discrete Mathematics; Vol 4, No 3 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/924/453 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-03-21T06:47:49Z
collection OJS
language English
topic semigroup of matrix units
semitopological semigroup
topological semigroup
topological inverse semigroup
\(H\)-closed semigroup
absolutely \(H\)-closed semigroup
algebraically \(h\)-closed semigroup
Bohr compactification
20M15
20M18
22A15
54A10
54C25
54D25
54D35
54H10
spellingShingle semigroup of matrix units
semitopological semigroup
topological semigroup
topological inverse semigroup
\(H\)-closed semigroup
absolutely \(H\)-closed semigroup
algebraically \(h\)-closed semigroup
Bohr compactification
20M15
20M18
22A15
54A10
54C25
54D25
54D35
54H10
Gutik, Oleg V.
Pavlyk, Kateryna P.
Topological semigroups of matrix units
topic_facet semigroup of matrix units
semitopological semigroup
topological semigroup
topological inverse semigroup
\(H\)-closed semigroup
absolutely \(H\)-closed semigroup
algebraically \(h\)-closed semigroup
Bohr compactification
20M15
20M18
22A15
54A10
54C25
54D25
54D35
54H10
format Article
author Gutik, Oleg V.
Pavlyk, Kateryna P.
author_facet Gutik, Oleg V.
Pavlyk, Kateryna P.
author_sort Gutik, Oleg V.
title Topological semigroups of matrix units
title_short Topological semigroups of matrix units
title_full Topological semigroups of matrix units
title_fullStr Topological semigroups of matrix units
title_full_unstemmed Topological semigroups of matrix units
title_sort topological semigroups of matrix units
description We prove that the semigroup of matrix units is stable. Compact, countably compact and pseudocompact topologies \(\tau\) on the infinite semigroup of matrix units \(B_\lambda\) such that \((B_\lambda,\tau)\) is a semitopological (inverse) semigroup are described. We prove the following properties of an infinite topological semigroup of matrix units. On the infinite semigroup of matrix units there exists no semigroup pseudocompact topology. Any continuous homomorphism from the infinite topological semigroup of matrix units into a compact topological semigroup is annihilating. The semigroup of matrix units is algebraically \(h\)-closed in the class of topological inverse semigroups. Some \(H\)-closed minimal semigroup topologies on the infinite semigroup of matrix units are considered.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/924
work_keys_str_mv AT gutikolegv topologicalsemigroupsofmatrixunits
AT pavlykkaterynap topologicalsemigroupsofmatrixunits
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