On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images
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| Creator |
Gutik, O.
Pozdnyakova, I. |
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| 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.
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| Date |
2019-06-14T03:23:31Z
2019-06-14T03:23:31Z 2014 |
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| Type |
Article
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| Identifier |
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. http://dspace.nbuv.gov.ua/handle/123456789/153337 |
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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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