Presentations and word problem for strong semilattices of semigroups
Let \(I\) be a semilattice, and \(S_i\) \((i\in I)\) be a family of disjoint semigroups. Then we prove that the strong semilattice \(S=\mathcal{S} [I,S_i,\phi _{j,i}]\) of semigroups \(S_i\) with homomorphisms \(\phi _{j,i}:S_j\rightarrow S_i\) (\(j\geq i\)) is finitely presented if and only if \(I\...
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| Дата: | 2018 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/943 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543412422967296 |
|---|---|
| author | Ayık, Gonca Ayık, Hayrullah Unlu, Yusuf |
| author_facet | Ayık, Gonca Ayık, Hayrullah Unlu, Yusuf |
| author_sort | Ayık, Gonca |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T06:49:56Z |
| description | Let \(I\) be a semilattice, and \(S_i\) \((i\in I)\) be a family of disjoint semigroups. Then we prove that the strong semilattice \(S=\mathcal{S} [I,S_i,\phi _{j,i}]\) of semigroups \(S_i\) with homomorphisms \(\phi _{j,i}:S_j\rightarrow S_i\) (\(j\geq i\)) is finitely presented if and only if \(I\) is finite and each \(S_i\) \((i\in I)\) is finitely presented. Moreover, for a finite semilattice \(I\), \(S\) has a soluble word problem if and only if each \(S_i\) \((i\in I)\) has a soluble word problem. Finally, we give an example of non-automatic semigroup which has a soluble word problem. |
| first_indexed | 2025-12-02T15:43:41Z |
| format | Article |
| id | admjournalluguniveduua-article-943 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:43:41Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-9432018-03-21T06:49:56Z Presentations and word problem for strong semilattices of semigroups Ayık, Gonca Ayık, Hayrullah Unlu, Yusuf Semigroup presentations, strong semilattices of semigroups, word problems 20M05 Let \(I\) be a semilattice, and \(S_i\) \((i\in I)\) be a family of disjoint semigroups. Then we prove that the strong semilattice \(S=\mathcal{S} [I,S_i,\phi _{j,i}]\) of semigroups \(S_i\) with homomorphisms \(\phi _{j,i}:S_j\rightarrow S_i\) (\(j\geq i\)) is finitely presented if and only if \(I\) is finite and each \(S_i\) \((i\in I)\) is finitely presented. Moreover, for a finite semilattice \(I\), \(S\) has a soluble word problem if and only if each \(S_i\) \((i\in I)\) has a soluble word problem. Finally, we give an example of non-automatic semigroup which has a soluble word problem. 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/943 Algebra and Discrete Mathematics; Vol 4, No 4 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/943/472 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Semigroup presentations strong semilattices of semigroups word problems 20M05 Ayık, Gonca Ayık, Hayrullah Unlu, Yusuf Presentations and word problem for strong semilattices of semigroups |
| title | Presentations and word problem for strong semilattices of semigroups |
| title_full | Presentations and word problem for strong semilattices of semigroups |
| title_fullStr | Presentations and word problem for strong semilattices of semigroups |
| title_full_unstemmed | Presentations and word problem for strong semilattices of semigroups |
| title_short | Presentations and word problem for strong semilattices of semigroups |
| title_sort | presentations and word problem for strong semilattices of semigroups |
| topic | Semigroup presentations strong semilattices of semigroups word problems 20M05 |
| topic_facet | Semigroup presentations strong semilattices of semigroups word problems 20M05 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/943 |
| work_keys_str_mv | AT ayıkgonca presentationsandwordproblemforstrongsemilatticesofsemigroups AT ayıkhayrullah presentationsandwordproblemforstrongsemilatticesofsemigroups AT unluyusuf presentationsandwordproblemforstrongsemilatticesofsemigroups |