A Class of Congruencies on Distributive Semilattice
In this paper we, contribute the notation of natural epimorphism of a semilattice on the quotient semilattice and subsemilattice. If S is distributive semilattice and F is a filter of S, then we demonstrate that θF is the smallest congruence on S containing F in a single equivalence class and that...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | Spanish |
| Published: |
Universidad del Quindio
2022-12-01
|
| Series: | Revista de Investigaciones Universidad del Quindío |
| Subjects: | |
| Online Access: | http://revistas.uniquindio.edu.co/ojs/index.php/riuq/article/view/525 |
| _version_ | 1797975466309582848 |
|---|---|
| author | Tolesa Dekeba Bekele Tesfu Reta |
| author_facet | Tolesa Dekeba Bekele Tesfu Reta |
| author_sort | Tolesa Dekeba Bekele |
| collection | DOAJ |
| description |
In this paper we, contribute the notation of natural epimorphism of a semilattice on the quotient semilattice and subsemilattice. If S is distributive semilattice and F is a filter of S, then we demonstrate that θF is the smallest congruence on S containing F in a single equivalence class and that S/θF is distributive. In addition, the author proved that map FθF is an isomorphism from the lattice of F0(S) all non-empty filters of S into a permutable sublattice of the lattice C(S) of all congruencies on S.
|
| first_indexed | 2024-04-11T04:36:00Z |
| format | Article |
| id | doaj.art-8906e96ba2104153a29dbc20c79c5571 |
| institution | Directory Open Access Journal |
| issn | 1794-631X 2500-5782 |
| language | Spanish |
| last_indexed | 2024-04-11T04:36:00Z |
| publishDate | 2022-12-01 |
| publisher | Universidad del Quindio |
| record_format | Article |
| series | Revista de Investigaciones Universidad del Quindío |
| spelling | doaj.art-8906e96ba2104153a29dbc20c79c55712022-12-28T16:15:08ZspaUniversidad del QuindioRevista de Investigaciones Universidad del Quindío1794-631X2500-57822022-12-0134110.33975/riuq.vol34n1.525A Class of Congruencies on Distributive SemilatticeTolesa Dekeba Bekele0Tesfu Reta1Dire Dawa UniversityDire Dawa University In this paper we, contribute the notation of natural epimorphism of a semilattice on the quotient semilattice and subsemilattice. If S is distributive semilattice and F is a filter of S, then we demonstrate that θF is the smallest congruence on S containing F in a single equivalence class and that S/θF is distributive. In addition, the author proved that map FθF is an isomorphism from the lattice of F0(S) all non-empty filters of S into a permutable sublattice of the lattice C(S) of all congruencies on S. http://revistas.uniquindio.edu.co/ojs/index.php/riuq/article/view/525Congruence class of semilatticeDistributive SemilatticeNatural epimorphism of semilatticeQuotient semilattice |
| spellingShingle | Tolesa Dekeba Bekele Tesfu Reta A Class of Congruencies on Distributive Semilattice Revista de Investigaciones Universidad del Quindío Congruence class of semilattice Distributive Semilattice Natural epimorphism of semilattice Quotient semilattice |
| title | A Class of Congruencies on Distributive Semilattice |
| title_full | A Class of Congruencies on Distributive Semilattice |
| title_fullStr | A Class of Congruencies on Distributive Semilattice |
| title_full_unstemmed | A Class of Congruencies on Distributive Semilattice |
| title_short | A Class of Congruencies on Distributive Semilattice |
| title_sort | class of congruencies on distributive semilattice |
| topic | Congruence class of semilattice Distributive Semilattice Natural epimorphism of semilattice Quotient semilattice |
| url | http://revistas.uniquindio.edu.co/ojs/index.php/riuq/article/view/525 |
| work_keys_str_mv | AT tolesadekebabekele aclassofcongruenciesondistributivesemilattice AT tesfureta aclassofcongruenciesondistributivesemilattice AT tolesadekebabekele classofcongruenciesondistributivesemilattice AT tesfureta classofcongruenciesondistributivesemilattice |