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\...
Збережено в:
| Видавець: | Lugansk National Taras Shevchenko University |
|---|---|
| Дата: | 2018 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/943 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
Репозиторії
Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-943 |
|---|---|
| record_format |
ojs |
| spelling |
oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| collection |
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 |
| work_keys_str_mv |
AT ayıkgonca presentationsandwordproblemforstrongsemilatticesofsemigroups AT ayıkhayrullah presentationsandwordproblemforstrongsemilatticesofsemigroups AT unluyusuf presentationsandwordproblemforstrongsemilatticesofsemigroups |
| first_indexed |
2024-04-12T06:27:32Z |
| last_indexed |
2024-04-12T06:27:32Z |
| _version_ |
1796109256360984576 |