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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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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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/943 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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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 |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2018-03-21T06:49:56Z |
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OJS |
| language |
English |
| topic |
Semigroup presentations strong semilattices of semigroups word problems 20M05 |
| 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 |
| topic_facet |
Semigroup presentations strong semilattices of semigroups word problems 20M05 |
| format |
Article |
| author |
Ayık, Gonca Ayık, Hayrullah Unlu, Yusuf |
| author_facet |
Ayık, Gonca Ayık, Hayrullah Unlu, Yusuf |
| author_sort |
Ayık, Gonca |
| title |
Presentations and word problem for strong semilattices of semigroups |
| title_short |
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_sort |
presentations and word problem for strong semilattices of semigroups |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/943 |
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AT ayıkgonca presentationsandwordproblemforstrongsemilatticesofsemigroups AT ayıkhayrullah presentationsandwordproblemforstrongsemilatticesofsemigroups AT unluyusuf presentationsandwordproblemforstrongsemilatticesofsemigroups |
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2025-12-02T15:43:41Z |
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2025-12-02T15:43:41Z |
| _version_ |
1850411813619892224 |