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On a semitopological polycyclic monoid

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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Main Authors: Bardyla, S., Gutik, O.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2016
Series:Algebra and Discrete Mathematics
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/155255
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spelling irk-123456789-1552552019-06-17T01:26:58Z On a semitopological polycyclic monoid Bardyla, S. Gutik, O. 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. 2016 Article 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 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Bardyla, S.
Gutik, O.
spellingShingle Bardyla, S.
Gutik, O.
On a semitopological polycyclic monoid
Algebra and Discrete Mathematics
author_facet Bardyla, S.
Gutik, O.
author_sort Bardyla, S.
title On a semitopological polycyclic monoid
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
publisher Інститут прикладної математики і механіки НАН України
publishDate 2016
url http://dspace.nbuv.gov.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.
series Algebra and Discrete Mathematics
work_keys_str_mv AT bardylas onasemitopologicalpolycyclicmonoid
AT gutiko onasemitopologicalpolycyclicmonoid
first_indexed 2023-05-20T17:46:28Z
last_indexed 2023-05-20T17:46:28Z
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