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...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2016 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2016
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155255 |
| 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: | On a semitopological polycyclic monoid / S. Bardyla, O. Gutik // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 163-183. — Бібліогр.: 38 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-155255 |
|---|---|
| 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On a semitopological polycyclic monoid |
| spellingShingle |
On a semitopological polycyclic monoid Bardyla, S. Gutik, O. |
| title_short |
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_sort |
on a semitopological polycyclic monoid |
| author |
Bardyla, S. Gutik, O. |
| author_facet |
Bardyla, S. Gutik, O. |
| publishDate |
2016 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155255 |
| 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. |
| work_keys_str_mv |
AT bardylas onasemitopologicalpolycyclicmonoid AT gutiko onasemitopologicalpolycyclicmonoid |
| first_indexed |
2025-12-02T04:28:41Z |
| last_indexed |
2025-12-02T04:28:41Z |
| _version_ |
1850861551507996672 |