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 |
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| 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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nasplib_isofts_kiev_ua-123456789-155237 |
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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Representation of Steinitz's lattice in lattices of substructures of relational structures |
| spellingShingle |
Representation of Steinitz's lattice in lattices of substructures of relational structures Bezushchak, O. Oliynyk, B. Sushchansky, V. |
| 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 |
| author |
Bezushchak, O. Oliynyk, B. Sushchansky, V. |
| author_facet |
Bezushchak, O. Oliynyk, B. Sushchansky, V. |
| publishDate |
2016 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155237 |
| 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. |
| work_keys_str_mv |
AT bezushchako representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures AT oliynykb representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures AT sushchanskyv representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures |
| first_indexed |
2025-12-07T17:05:08Z |
| last_indexed |
2025-12-07T17:05:08Z |
| _version_ |
1850869922622603264 |