Presentations and word problem for strong semilattices of semigroups
Let I be a semilattice, and Si (i ∈ I) be a family of disjoint semigroups. Then we prove that the strong semilattice S = S[I, Si , φj,i] of semigroups Si with homomorphisms φj,i : Sj → Si (j ≥ i) is finitely presented if and only if I is finite and each Si (i ∈ I) is finitely presented. Moreove...
Збережено в:
| Дата: | 2005 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/157334 |
| Теги: |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Presentations and word problem for strong semilattices of semigroups / G. Ayık, H. Ayık, Y. Unlu // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 4. — С. 28–35. — Бібліогр.: 11 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | Let I be a semilattice, and Si (i ∈ I) be a family
of disjoint semigroups. Then we prove that the strong semilattice
S = S[I, Si
, φj,i] of semigroups Si with homomorphisms φj,i : Sj →
Si (j ≥ i) is finitely presented if and only if I is finite and each
Si (i ∈ I) is finitely presented. Moreover, for a finite semilattice
I, S has a soluble word problem if and only if each Si (i ∈ I)
has a soluble word problem. Finally, we give an example of nonautomatic semigroup which has a soluble word problem. |
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