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.
Збережено в:
| Дата: | 2010 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2010
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154609 |
| Теги: |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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