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:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2018
|
| Online Zugang: | https://nasplib.isofts.kiev.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| _version_ | 1862616292423368704 |
|---|---|
| author | Jakubíková-Studenovská, D. Janičková, L. |
| author_facet | Jakubíková-Studenovská, D. Janičková, L. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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 (*).
|
| first_indexed | 2025-12-07T13:09:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188347 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T13:09:16Z |
| publishDate | 2018 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Jakubíková-Studenovská, D. Janičková, L. 2023-02-23T19:23:10Z 2023-02-23T19:23:10Z 2018 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. https://nasplib.isofts.kiev.ua/handle/123456789/188347 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 (*). This work was supported by Grant VEGA 1/0063/14 and VEGA 1/0097/18. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Construction of a complementary quasiorder Article published earlier |
| spellingShingle | Construction of a complementary quasiorder Jakubíková-Studenovská, D. Janičková, L. |
| title | 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_short | Construction of a complementary quasiorder |
| title_sort | construction of a complementary quasiorder |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188347 |
| work_keys_str_mv | AT jakubikovastudenovskad constructionofacomplementaryquasiorder AT janickoval constructionofacomplementaryquasiorder |