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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Published in:Algebra and Discrete Mathematics
Date:2016
Main Authors: Bezushchak, O., Oliynyk, B., Sushchansky, V.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2016
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/155237
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Representation of Steinitz's lattice in lattices of substructures of relational structures / O. Bezushchak, B. Oliynyk, V. Sushchansky // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 184-201. — Бібліогр.: 19 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Bezushchak, O.
Oliynyk, B.
Sushchansky, V.
author_facet Bezushchak, O.
Oliynyk, B.
Sushchansky, V.
citation_txt Representation of Steinitz's lattice in lattices of substructures of relational structures / O. Bezushchak, B. Oliynyk, V. Sushchansky // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 184-201. — Бібліогр.: 19 назв. — англ.
collection DSpace DC
container_title Algebra and Discrete Mathematics
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 2025-12-07T17:05:08Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1726-3255
language English
last_indexed 2025-12-07T17:05:08Z
publishDate 2016
publisher Інститут прикладної математики і механіки НАН України
record_format dspace
spelling Bezushchak, O.
Oliynyk, B.
Sushchansky, V.
2019-06-16T14:26:24Z
2019-06-16T14:26:24Z
2016
Representation of Steinitz's lattice in lattices of substructures of relational structures / O. Bezushchak, B. Oliynyk, V. Sushchansky // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 184-201. — Бібліогр.: 19 назв. — англ.
1726-3255
2010 MSC:03G10, 08A02, 03G05.
https://nasplib.isofts.kiev.ua/handle/123456789/155237
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.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Representation of Steinitz's lattice in lattices of substructures of relational structures
Article
published earlier
spellingShingle Representation of Steinitz's lattice in lattices of substructures of relational structures
Bezushchak, O.
Oliynyk, B.
Sushchansky, V.
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
url https://nasplib.isofts.kiev.ua/handle/123456789/155237
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AT oliynykb representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures
AT sushchanskyv representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures