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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| Datum: | 2018 |
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| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | 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| _version_ | 1856543326053859328 |
|---|---|
| author | Gutik, Oleg V. Pavlyk, Kateryna P. |
| author_facet | Gutik, Oleg V. Pavlyk, Kateryna P. |
| author_sort | Gutik, Oleg V. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T06:47:49Z |
| 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. |
| first_indexed | 2025-12-02T15:45:16Z |
| format | Article |
| id | admjournalluguniveduua-article-924 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:45:16Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| 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 |
| 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 |
| title | 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_short | Topological semigroups of matrix units |
| title_sort | topological semigroups of matrix units |
| 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 |
| 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 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/924 |
| work_keys_str_mv | AT gutikolegv topologicalsemigroupsofmatrixunits AT pavlykkaterynap topologicalsemigroupsofmatrixunits |