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 |
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| Date: | 2016 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2016
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| 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| _version_ | 1862707408145481728 |
|---|---|
| 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.
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| first_indexed | 2025-12-07T17:05:08Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-155237 |
| 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 |
| work_keys_str_mv | AT bezushchako representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures AT oliynykb representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures AT sushchanskyv representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures |