Generators and relations for the semigroups of increasing functions on \(\mathbb{N}\) and \(\mathbb{Z}\)
The semigroups of all increasing functions over \(\mathbb{N}\) and \(\mathbb{Z}\) are considered. It is shown that both these semigroups do not admit an irreducible system of generators. In their subsemigroups of cofinite functions all irreducible systems of generators are described. The last semi...
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/941 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543278845919232 |
|---|---|
| author | Doroshenko, Vadym |
| author_facet | Doroshenko, Vadym |
| author_sort | Doroshenko, Vadym |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T06:49:56Z |
| description | The semigroups of all increasing functions over \(\mathbb{N}\) and \(\mathbb{Z}\) are considered. It is shown that both these semigroups do not admit an irreducible system of generators. In their subsemigroups of cofinite functions all irreducible systems of generators are described. The last semigroups are presented in terms of generators and relations. |
| first_indexed | 2026-02-08T08:00:41Z |
| format | Article |
| id | admjournalluguniveduua-article-941 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:00:41Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-9412018-03-21T06:49:56Z Generators and relations for the semigroups of increasing functions on \(\mathbb{N}\) and \(\mathbb{Z}\) Doroshenko, Vadym Order-preserving transformation, monotonic function, generating system, generators and relations, word problem 20M05, 20M20 The semigroups of all increasing functions over \(\mathbb{N}\) and \(\mathbb{Z}\) are considered. It is shown that both these semigroups do not admit an irreducible system of generators. In their subsemigroups of cofinite functions all irreducible systems of generators are described. The last semigroups are presented in terms of generators and relations. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/941 Algebra and Discrete Mathematics; Vol 4, No 4 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/941/470 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Order-preserving transformation monotonic function generating system generators and relations word problem 20M05 20M20 Doroshenko, Vadym Generators and relations for the semigroups of increasing functions on \(\mathbb{N}\) and \(\mathbb{Z}\) |
| title | Generators and relations for the semigroups of increasing functions on \(\mathbb{N}\) and \(\mathbb{Z}\) |
| title_full | Generators and relations for the semigroups of increasing functions on \(\mathbb{N}\) and \(\mathbb{Z}\) |
| title_fullStr | Generators and relations for the semigroups of increasing functions on \(\mathbb{N}\) and \(\mathbb{Z}\) |
| title_full_unstemmed | Generators and relations for the semigroups of increasing functions on \(\mathbb{N}\) and \(\mathbb{Z}\) |
| title_short | Generators and relations for the semigroups of increasing functions on \(\mathbb{N}\) and \(\mathbb{Z}\) |
| title_sort | generators and relations for the semigroups of increasing functions on \(\mathbb{n}\) and \(\mathbb{z}\) |
| topic | Order-preserving transformation monotonic function generating system generators and relations word problem 20M05 20M20 |
| topic_facet | Order-preserving transformation monotonic function generating system generators and relations word problem 20M05 20M20 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/941 |
| work_keys_str_mv | AT doroshenkovadym generatorsandrelationsforthesemigroupsofincreasingfunctionsonmathbbnandmathbbz |