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
 S...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2005 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2005
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| Online Zugang: | https://nasplib.isofts.kiev.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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862556742534037504 |
|---|---|
| author | Ayık, G. Ayık, H. Unlu, Y. |
| author_facet | Ayık, G. Ayık, H. Unlu, Y. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-11-25T22:33:41Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-157334 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-25T22:33:41Z |
| publishDate | 2005 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Ayık, G. Ayık, H. Unlu, Y. 2019-06-20T02:30:48Z 2019-06-20T02:30:48Z 2005 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. https://nasplib.isofts.kiev.ua/handle/123456789/157334 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Presentations and word problem for strong semilattices of semigroups Article published earlier |
| spellingShingle | Presentations and word problem for strong semilattices of semigroups Ayık, G. Ayık, H. Unlu, Y. |
| title | 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_short | Presentations and word problem for strong semilattices of semigroups |
| title_sort | presentations and word problem for strong semilattices of semigroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/157334 |
| work_keys_str_mv | AT ayıkg presentationsandwordproblemforstrongsemilatticesofsemigroups AT ayıkh presentationsandwordproblemforstrongsemilatticesofsemigroups AT unluy presentationsandwordproblemforstrongsemilatticesofsemigroups |