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 i...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2005 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2005
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/157194 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862686469718540288 |
|---|---|
| author | Gutik, O.V. Pavlyk, K.P. |
| author_facet | Gutik, O.V. Pavlyk, K.P. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T16:03:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-157194 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:03:40Z |
| publishDate | 2005 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Topological semigroups of matrix units Gutik, O.V. Pavlyk, K.P. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/157194 |
| work_keys_str_mv | AT gutikov topologicalsemigroupsofmatrixunits AT pavlykkp topologicalsemigroupsofmatrixunits |