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: Banakh, T., Protasov, I.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2010
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
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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
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1726-3255
language English
last_indexed 2025-12-07T17:34:33Z
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