Representation of Steinitz's lattice in lattices of substructures of relational structures
General conditions under which certain relational structure contains a lattice of substructures isomorphic to Steinitz's lattice are formulated. Under some natural restrictions we consider relational structures with the lattice containing a sublattice isomorphic to the lattice of positive integ...
Gespeichert in:
| Datum: | 2016 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2016
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/250 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| _version_ | 1856543061767618560 |
|---|---|
| author | Bezushchak, Oksana Oliynyk, Bogdana Sushchansky, Vitaliy |
| author_facet | Bezushchak, Oksana Oliynyk, Bogdana Sushchansky, Vitaliy |
| author_sort | Bezushchak, Oksana |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2016-07-12T10:09:40Z |
| description | General conditions under which certain relational structure contains a lattice of substructures isomorphic to Steinitz's lattice are formulated. Under some natural restrictions we consider relational structures with the lattice containing a sublattice isomorphic to the lattice of positive integers with respect to divisibility. We apply to this sublattice a construction that could be called ``lattice completion''. This construction can be used for different types of relational structures, in particular for universal algebras, graphs, metric spaces etc. Some examples are considered. |
| first_indexed | 2025-12-02T15:31:22Z |
| format | Article |
| id | admjournalluguniveduua-article-250 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:31:22Z |
| publishDate | 2016 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-2502016-07-12T10:09:40Z Representation of Steinitz's lattice in lattices of substructures of relational structures Bezushchak, Oksana Oliynyk, Bogdana Sushchansky, Vitaliy relational structure, lattice, supernatural numbers, Boolean algebra 03G10, 08A02, 03G05 General conditions under which certain relational structure contains a lattice of substructures isomorphic to Steinitz's lattice are formulated. Under some natural restrictions we consider relational structures with the lattice containing a sublattice isomorphic to the lattice of positive integers with respect to divisibility. We apply to this sublattice a construction that could be called ``lattice completion''. This construction can be used for different types of relational structures, in particular for universal algebras, graphs, metric spaces etc. Some examples are considered. Lugansk National Taras Shevchenko University 2016-07-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/250 Algebra and Discrete Mathematics; Vol 21, No 2 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/250/61 Copyright (c) 2016 Algebra and Discrete Mathematics |
| spellingShingle | relational structure lattice supernatural numbers Boolean algebra 03G10 08A02 03G05 Bezushchak, Oksana Oliynyk, Bogdana Sushchansky, Vitaliy Representation of Steinitz's lattice in lattices of substructures of relational structures |
| title | Representation of Steinitz's lattice in lattices of substructures of relational structures |
| title_full | Representation of Steinitz's lattice in lattices of substructures of relational structures |
| title_fullStr | Representation of Steinitz's lattice in lattices of substructures of relational structures |
| title_full_unstemmed | Representation of Steinitz's lattice in lattices of substructures of relational structures |
| title_short | Representation of Steinitz's lattice in lattices of substructures of relational structures |
| title_sort | representation of steinitz's lattice in lattices of substructures of relational structures |
| topic | relational structure lattice supernatural numbers Boolean algebra 03G10 08A02 03G05 |
| topic_facet | relational structure lattice supernatural numbers Boolean algebra 03G10 08A02 03G05 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/250 |
| work_keys_str_mv | AT bezushchakoksana representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures AT oliynykbogdana representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures AT sushchanskyvitaliy representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures |