Partitions of groups and matroids into independent subsets
Can the set R∖{0} be covered by countably many linearly (algebraically) independent subsets over the field Q? We use a matroid approach to show that an answer is ``Yes'' under the Continuum Hypothesis, and ``No'' under its negation.
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2010 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154609 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Partitions of groups and matroids into independent subsets / T. Banakh, I. Protasov // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 1–7. — Бібліогр.: 4 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712127195709440 |
|---|---|
| author | Banakh, T. Protasov, I. |
| author_facet | Banakh, T. Protasov, I. |
| citation_txt | Partitions of groups and matroids into independent subsets / T. Banakh, I. Protasov // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 1–7. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Can the set R∖{0} be covered by countably many linearly (algebraically) independent subsets over the field Q? We use a matroid approach to show that an answer is ``Yes'' under the Continuum Hypothesis, and ``No'' under its negation.
|
| first_indexed | 2025-12-07T17:34:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154609 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T17:34:33Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Banakh, T. Protasov, I. 2019-06-15T16:50:24Z 2019-06-15T16:50:24Z 2010 Partitions of groups and matroids into independent subsets / T. Banakh, I. Protasov // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 1–7. — Бібліогр.: 4 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:05B35, 05A18. https://nasplib.isofts.kiev.ua/handle/123456789/154609 Can the set R∖{0} be covered by countably many linearly (algebraically) independent subsets over the field Q? We use a matroid approach to show that an answer is ``Yes'' under the Continuum Hypothesis, and ``No'' under its negation. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Partitions of groups and matroids into independent subsets Article published earlier |
| spellingShingle | Partitions of groups and matroids into independent subsets Banakh, T. Protasov, I. |
| title | Partitions of groups and matroids into independent subsets |
| title_full | Partitions of groups and matroids into independent subsets |
| title_fullStr | Partitions of groups and matroids into independent subsets |
| title_full_unstemmed | Partitions of groups and matroids into independent subsets |
| title_short | Partitions of groups and matroids into independent subsets |
| title_sort | partitions of groups and matroids into independent subsets |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154609 |
| work_keys_str_mv | AT banakht partitionsofgroupsandmatroidsintoindependentsubsets AT protasovi partitionsofgroupsandmatroidsintoindependentsubsets |