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...
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| Datum: | 2005 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2005
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/157334 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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irk-123456789-1573342019-06-21T01:26:43Z Presentations and word problem for strong semilattices of semigroups Ayık, G. Ayık, H. Unlu, Y. 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. 2005 Article 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. 1726-3255 2000 Mathematics Subject Classification: 20M05. http://dspace.nbuv.gov.ua/handle/123456789/157334 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Ayık, G. Ayık, H. Unlu, Y. |
| spellingShingle |
Ayık, G. Ayık, H. Unlu, Y. Presentations and word problem for strong semilattices of semigroups Algebra and Discrete Mathematics |
| author_facet |
Ayık, G. Ayık, H. Unlu, Y. |
| author_sort |
Ayık, G. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/157334 |
| citation_txt |
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. |
| series |
Algebra and Discrete Mathematics |
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2025-07-14T09:46:42Z |
| last_indexed |
2025-07-14T09:46:42Z |
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1837615181847330816 |