On a semitopological polycyclic monoid
We study algebraic structure of the λ-polycyclic monoid Pλ and its topologizations. We show that the λ-polycyclic monoid for an infinite cardinal λ≥2 has similar algebraic properties so has the polycyclic monoid Pn with finitely many n≥2 generators. In particular we prove that for every infinite car...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155255 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On a semitopological polycyclic monoid / S. Bardyla, O. Gutik // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 163-183. — Бібліогр.: 38 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862656413737680896 |
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| author | Bardyla, S. Gutik, O. |
| author_facet | Bardyla, S. Gutik, O. |
| citation_txt | On a semitopological polycyclic monoid / S. Bardyla, O. Gutik // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 163-183. — Бібліогр.: 38 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | We study algebraic structure of the λ-polycyclic monoid Pλ and its topologizations. We show that the λ-polycyclic monoid for an infinite cardinal λ≥2 has similar algebraic properties so has the polycyclic monoid Pn with finitely many n≥2 generators. In particular we prove that for every infinite cardinal λ the polycyclic monoid Pλ is a congruence-free combinatorial 0-bisimple 0-E-unitary inverse semigroup. Also we show that every non-zero element x is an isolated point in (Pλ,τ) for every Hausdorff topology τ on Pλ, such that (Pλ,τ) is a semitopological semigroup, and every locally compact Hausdorff semigroup topology on Pλ is discrete. The last statement extends results of the paper [33] obtaining for topological inverse graph semigroups. We describe all feebly compact topologies τ on Pλ such that (Pλ,τ) is a semitopological semigroup and its Bohr compactification as a topological semigroup. We prove that for every cardinal λ≥2 any continuous homomorphism from a topological semigroup Pλ into an arbitrary countably compact topological semigroup is annihilating and there exists no a Hausdorff feebly compact topological semigroup which contains Pλ as a dense subsemigroup.
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| first_indexed | 2025-12-02T04:28:41Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155255 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-02T04:28:41Z |
| publishDate | 2016 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Bardyla, S. Gutik, O. 2019-06-16T14:49:31Z 2019-06-16T14:49:31Z 2016 On a semitopological polycyclic monoid / S. Bardyla, O. Gutik // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 163-183. — Бібліогр.: 38 назв. — англ. 1726-3255 2010 MSC:Primary 22A15, 20M18. Secondary 20M05, 22A26, 54A10, 54D30,54D35, 54D45, 54H11. https://nasplib.isofts.kiev.ua/handle/123456789/155255 We study algebraic structure of the λ-polycyclic monoid Pλ and its topologizations. We show that the λ-polycyclic monoid for an infinite cardinal λ≥2 has similar algebraic properties so has the polycyclic monoid Pn with finitely many n≥2 generators. In particular we prove that for every infinite cardinal λ the polycyclic monoid Pλ is a congruence-free combinatorial 0-bisimple 0-E-unitary inverse semigroup. Also we show that every non-zero element x is an isolated point in (Pλ,τ) for every Hausdorff topology τ on Pλ, such that (Pλ,τ) is a semitopological semigroup, and every locally compact Hausdorff semigroup topology on Pλ is discrete. The last statement extends results of the paper [33] obtaining for topological inverse graph semigroups. We describe all feebly compact topologies τ on Pλ such that (Pλ,τ) is a semitopological semigroup and its Bohr compactification as a topological semigroup. We prove that for every cardinal λ≥2 any continuous homomorphism from a topological semigroup Pλ into an arbitrary countably compact topological semigroup is annihilating and there exists no a Hausdorff feebly compact topological semigroup which contains Pλ as a dense subsemigroup. We acknowledge Alex Ravsky for his comments and suggestions. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On a semitopological polycyclic monoid Article published earlier |
| spellingShingle | On a semitopological polycyclic monoid Bardyla, S. Gutik, O. |
| title | On a semitopological polycyclic monoid |
| title_full | On a semitopological polycyclic monoid |
| title_fullStr | On a semitopological polycyclic monoid |
| title_full_unstemmed | On a semitopological polycyclic monoid |
| title_short | On a semitopological polycyclic monoid |
| title_sort | on a semitopological polycyclic monoid |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155255 |
| work_keys_str_mv | AT bardylas onasemitopologicalpolycyclicmonoid AT gutiko onasemitopologicalpolycyclicmonoid |