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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| Дата: | 2016 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2016
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/155237 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-155237 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1552372019-06-17T01:28:27Z Representation of Steinitz's lattice in lattices of substructures of relational structures Bezushchak, O. Oliynyk, B. Sushchansky, V. 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. 2016 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/155237 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Bezushchak, O. Oliynyk, B. Sushchansky, V. |
| spellingShingle |
Bezushchak, O. Oliynyk, B. Sushchansky, V. Representation of Steinitz's lattice in lattices of substructures of relational structures Algebra and Discrete Mathematics |
| author_facet |
Bezushchak, O. Oliynyk, B. Sushchansky, V. |
| author_sort |
Bezushchak, O. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT bezushchako representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures AT oliynykb representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures AT sushchanskyv representationofsteinitzslatticeinlatticesofsubstructuresofrelationalstructures |
| first_indexed |
2023-05-20T17:46:24Z |
| last_indexed |
2023-05-20T17:46:24Z |
| _version_ |
1796154059192795136 |