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...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2014
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/153337 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862631315792199680 |
|---|---|
| author | Gutik, O. Pozdnyakova, I. |
| author_facet | Gutik, O. Pozdnyakova, I. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-11-30T11:10:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-153337 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-30T11:10:09Z |
| publishDate | 2014 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | On monoids of monotone injective partial selfmaps of Ln ×lex Z with co-finite domains and images Gutik, O. Pozdnyakova, I. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/153337 |
| work_keys_str_mv | AT gutiko onmonoidsofmonotoneinjectivepartialselfmapsoflnlexzwithcofinitedomainsandimages AT pozdnyakovai onmonoidsofmonotoneinjectivepartialselfmapsoflnlexzwithcofinitedomainsandimages |