On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images
We study the semigroup IO∞(Zⁿlex) of monotone injective partial selfmaps of the set of Ln × lex Z having co-finite domain and image, where Ln ×lex Z is the lexicographic product of n-elements chain and the set of integers with the usual order. We show that IO∞(Zⁿlex) is bisimple and establish its pr...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2014 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/153337 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images / O. Gutik, I. Pozdnyakova // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 256–279. — Бібліогр.: 28 назв. — англ. |
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Gutik, O. Pozdnyakova, I. 2019-06-14T03:23:31Z 2019-06-14T03:23:31Z 2014 On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images / O. Gutik, I. Pozdnyakova // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 256–279. — Бібліогр.: 28 назв. — англ. 1726-3255 2010 MSC:20M18, 20M20; 20M05, 20M15, 22A15, 54C25, 54D40, 54E52, 54H10. https://nasplib.isofts.kiev.ua/handle/123456789/153337 We study the semigroup IO∞(Zⁿlex) of monotone injective partial selfmaps of the set of Ln × lex Z having co-finite domain and image, where Ln ×lex Z is the lexicographic product of n-elements chain and the set of integers with the usual order. We show that IO∞(Zⁿlex) is bisimple and establish its projective congruences. We prove that IO∞(Zⁿlex) is finitely generated, and for n = 1 every automorphism of IO∞(Zⁿlex) is inner and show that in the case n ⩾ 2 the semigroup IO∞(Zⁿlex) has non-inner automorphisms. Also we show that every Baire topology τ on IO∞(Znlex) such that (IO∞(Znlex),τ) is a Hausdorff semitopological semigroup is discrete, construct a non-discrete Hausdorff semigroup inverse topology on IO∞(Zⁿlex), and prove that the discrete semigroup IO∞(Zⁿlex) cannot be embedded into some classes of compact-like topological semigroups and that its remainder under the closure in a topological semigroup S is an ideal in S. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images |
| spellingShingle |
On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images Gutik, O. Pozdnyakova, I. |
| title_short |
On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images |
| title_full |
On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images |
| title_fullStr |
On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images |
| title_full_unstemmed |
On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images |
| title_sort |
on monoids of monotone injective partial selfmaps of ln ×lex z with co-finite domains and images |
| author |
Gutik, O. Pozdnyakova, I. |
| author_facet |
Gutik, O. Pozdnyakova, I. |
| publishDate |
2014 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
We study the semigroup IO∞(Zⁿlex) of monotone injective partial selfmaps of the set of Ln × lex Z having co-finite domain and image, where Ln ×lex Z is the lexicographic product of n-elements chain and the set of integers with the usual order. We show that IO∞(Zⁿlex) is bisimple and establish its projective congruences. We prove that IO∞(Zⁿlex) is finitely generated, and for n = 1 every automorphism of IO∞(Zⁿlex) is inner and show that in the case n ⩾ 2 the semigroup IO∞(Zⁿlex) has non-inner automorphisms. Also we show that every Baire topology τ on IO∞(Znlex) such that (IO∞(Znlex),τ) is a Hausdorff semitopological semigroup is discrete, construct a non-discrete Hausdorff semigroup inverse topology on IO∞(Zⁿlex), and prove that the discrete semigroup IO∞(Zⁿlex) cannot be embedded into some classes of compact-like topological semigroups and that its remainder under the closure in a topological semigroup S is an ideal in S.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/153337 |
| citation_txt |
On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images / O. Gutik, I. Pozdnyakova // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 256–279. — Бібліогр.: 28 назв. — англ. |
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2025-11-30T11:10:09Z |
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2025-11-30T11:10:09Z |
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