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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| Видавець: | Інститут прикладної математики і механіки НАН України |
|---|---|
| Дата: | 2014 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2014
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/153337 |
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| Цитувати: | 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. |
Репозиторії
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irk-123456789-1533372019-06-15T01:28:29Z On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images Gutik, O. Pozdnyakova, I. 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. 2014 Article 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 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 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. |
| format |
Article |
| author |
Gutik, O. Pozdnyakova, I. |
| spellingShingle |
Gutik, O. Pozdnyakova, I. On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images Algebra and Discrete Mathematics |
| author_facet |
Gutik, O. Pozdnyakova, I. |
| author_sort |
Gutik, O. |
| title |
On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
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2023-05-20T17:38:29Z |
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2023-05-20T17:38:29Z |
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