Representation of Steinitz's lattice in lattices of substructures of relational structures

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...

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Bibliographic Details
Date:2016
Main Authors: Bezushchak, Oksana, Oliynyk, Bogdana, Sushchansky, Vitaliy
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2016
Subjects:
relational structure
lattice
supernatural numbers
Boolean algebra
03G10
08A02
03G05
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/250
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-250
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
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2016-07-12T10:09:40Z
collection OJS
language English
topic relational structure
lattice
supernatural numbers
Boolean algebra
03G10
08A02
03G05
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
topic_facet relational structure
lattice
supernatural numbers
Boolean algebra
03G10
08A02
03G05
format Article
author Bezushchak, Oksana
Oliynyk, Bogdana
Sushchansky, Vitaliy
author_facet Bezushchak, Oksana
Oliynyk, Bogdana
Sushchansky, Vitaliy
author_sort Bezushchak, Oksana
title 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_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_sort representation of steinitz's lattice in lattices of substructures of relational structures
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.
publisher Lugansk National Taras Shevchenko University
publishDate 2016
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
first_indexed 2025-12-02T15:31:22Z
last_indexed 2025-12-02T15:31:22Z
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