Presentations and word problem for strong semilattices of semigroups

• Date: 2018
• Main Authors: Ayık, Gonca, Ayık, Hayrullah, Unlu, Yusuf
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Semigroup presentations; strong semilattices of semigroups; word problems; 20M05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/943
• Journal Title: Algebra and Discrete Mathematics

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\...