On a semitopological polycyclic monoid
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On a semitopological polycyclic monoid
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| Creator |
Bardyla, S.
Gutik, O. |
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| 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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| Date |
2019-06-16T14:49:31Z
2019-06-16T14:49:31Z 2016 |
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| Type |
Article
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| Identifier |
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. http://dspace.nbuv.gov.ua/handle/123456789/155255 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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