Topological semigroups of matrix units
We prove that the semigroup of matrix units is stable. Compact, countably compact and pseudocompact topologies τ on the infinite semigroup of matrix units Bλ such that (Bλ,τ ) is a semitopological (inverse) semigroup are described. We prove the following properties of an infinite topological semi...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2005 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/157194 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Topological semigroups of matrix units / O.V. Gutik, K.P. Pavlyk // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 3. — С. 1–17. — Бібліогр.: 26 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-157194 |
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dspace |
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Gutik, O.V. Pavlyk, K.P. 2019-06-19T17:29:34Z 2019-06-19T17:29:34Z 2005 Topological semigroups of matrix units / O.V. Gutik, K.P. Pavlyk // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 3. — С. 1–17. — Бібліогр.: 26 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 20M15, 20M18, 22A15, 54A10, 54C25, 54D25, 54D35, 54H10. https://nasplib.isofts.kiev.ua/handle/123456789/157194 We prove that the semigroup of matrix units is stable. Compact, countably compact and pseudocompact topologies τ on the infinite semigroup of matrix units Bλ such that (Bλ,τ ) 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. The authors are deeply grateful to T. Banakh and I. Guran for useful discussions of the results of this paper. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Topological semigroups of matrix units Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Topological semigroups of matrix units |
| spellingShingle |
Topological semigroups of matrix units Gutik, O.V. Pavlyk, K.P. |
| 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 |
| author |
Gutik, O.V. Pavlyk, K.P. |
| author_facet |
Gutik, O.V. Pavlyk, K.P. |
| publishDate |
2005 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
We prove that the semigroup of matrix units is
stable. Compact, countably compact and pseudocompact topologies τ on the infinite semigroup of matrix units Bλ such that (Bλ,τ )
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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/157194 |
| citation_txt |
Topological semigroups of matrix units / O.V. Gutik, K.P. Pavlyk // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 3. — С. 1–17. — Бібліогр.: 26 назв. — англ. |
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AT gutikov topologicalsemigroupsofmatrixunits AT pavlykkp topologicalsemigroupsofmatrixunits |
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2025-12-07T16:03:40Z |
| last_indexed |
2025-12-07T16:03:40Z |
| _version_ |
1850866055314931712 |