Construction of a complementary quasiorder
For a monounary algebra A = (A, f) we study the lattice QuordA of all quasiorders of A, i.e., of all reflexive and transitive relations compatible with f. Monounary algebras (A, f) whose lattices of quasiorders are complemented were characterized in 2011 as follows: (*) f(x) is a cyclic element for...
Gespeichert in:
| Datum: | 2018 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2018
|
| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/188347 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Construction of a complementary quasiorder / D. Jakubíková-Studenovská, L. Janičková // Algebra and Discrete Mathematics. — 2018. — Vol. 25, № 1. — С. 39-55. — Бібліогр.: 4 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-188347 |
|---|---|
| record_format |
dspace |
| fulltext |
|
| spelling |
irk-123456789-1883472023-02-24T01:27:27Z Construction of a complementary quasiorder Jakubíková-Studenovská, D. Janičková, L. For a monounary algebra A = (A, f) we study the lattice QuordA of all quasiorders of A, i.e., of all reflexive and transitive relations compatible with f. Monounary algebras (A, f) whose lattices of quasiorders are complemented were characterized in 2011 as follows: (*) f(x) is a cyclic element for all x ∊ A, and all cycles have the same square-free number n of elements. Sufficiency of the condition (*) was proved by means of transfinite induction. Now we will describe a construction of a complement to a given quasiorder of (A, f) satisfying (*). 2018 Article Construction of a complementary quasiorder / D. Jakubíková-Studenovská, L. Janičková // Algebra and Discrete Mathematics. — 2018. — Vol. 25, № 1. — С. 39-55. — Бібліогр.: 4 назв. — англ. 1726-3255 2010 MSC: 08A60, 08A02. http://dspace.nbuv.gov.ua/handle/123456789/188347 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 |
For a monounary algebra A = (A, f) we study the lattice QuordA of all quasiorders of A, i.e., of all reflexive and transitive relations compatible with f. Monounary algebras (A, f) whose lattices of quasiorders are complemented were characterized in 2011 as follows: (*) f(x) is a cyclic element for all x ∊ A, and all cycles have the same square-free number n of elements. Sufficiency of the condition (*) was proved by means of transfinite induction. Now we will describe a construction of a complement to a given quasiorder of (A, f) satisfying (*). |
| format |
Article |
| author |
Jakubíková-Studenovská, D. Janičková, L. |
| spellingShingle |
Jakubíková-Studenovská, D. Janičková, L. Construction of a complementary quasiorder Algebra and Discrete Mathematics |
| author_facet |
Jakubíková-Studenovská, D. Janičková, L. |
| author_sort |
Jakubíková-Studenovská, D. |
| title |
Construction of a complementary quasiorder |
| title_short |
Construction of a complementary quasiorder |
| title_full |
Construction of a complementary quasiorder |
| title_fullStr |
Construction of a complementary quasiorder |
| title_full_unstemmed |
Construction of a complementary quasiorder |
| title_sort |
construction of a complementary quasiorder |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2018 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188347 |
| citation_txt |
Construction of a complementary quasiorder / D. Jakubíková-Studenovská, L. Janičková // Algebra and Discrete Mathematics. — 2018. — Vol. 25, № 1. — С. 39-55. — Бібліогр.: 4 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT jakubikovastudenovskad constructionofacomplementaryquasiorder AT janickoval constructionofacomplementaryquasiorder |
| first_indexed |
2025-07-16T10:22:06Z |
| last_indexed |
2025-07-16T10:22:06Z |
| _version_ |
1837798603489280000 |