An elementary description of K₁(R) without elementary matrices
Let R be a ring with unit. Passing to the colimit with respect to the standard inclusions GL(n,R) → GL(n+1,R) (which add a unit vector as new last row and column) yields, by definition, the stable linear group GL(R); the same result is obtained, up to isomorphism, when using the “opposite” inclusio...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188554 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | An elementary description of K₁(R) without elementary matrices / T. Hüttemann, Z. Zhang // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 79–82. — Бібліогр.: 1 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862751660851331072 |
|---|---|
| author | Hüttemann, T. Zhang, Z. |
| author_facet | Hüttemann, T. Zhang, Z. |
| citation_txt | An elementary description of K₁(R) without elementary matrices / T. Hüttemann, Z. Zhang // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 79–82. — Бібліогр.: 1 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let R be a ring with unit. Passing to the colimit with respect to the standard inclusions GL(n,R) → GL(n+1,R) (which add a unit vector as new last row and column) yields, by definition, the stable linear group GL(R); the same result is obtained, up to isomorphism, when using the “opposite” inclusions (which add a unit vector as new first row and column). In this note it is shown that passing to the colimit along both these families of inclusions simultaneously recovers the algebraic K-group K₁(R) = GL(R)/E(R) of R, giving an elementary description that does not involve elementary matrices explicitly.
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| first_indexed | 2025-12-07T21:12:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188554 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T21:12:32Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Hüttemann, T. Zhang, Z. 2023-03-05T17:27:51Z 2023-03-05T17:27:51Z 2020 An elementary description of K₁(R) without elementary matrices / T. Hüttemann, Z. Zhang // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 79–82. — Бібліогр.: 1 назв. — англ. 1726-3255 DOI:10.12958/adm1568 2010 MSC: Primary 19B99; Secondary 16E20 https://nasplib.isofts.kiev.ua/handle/123456789/188554 Let R be a ring with unit. Passing to the colimit with respect to the standard inclusions GL(n,R) → GL(n+1,R) (which add a unit vector as new last row and column) yields, by definition, the stable linear group GL(R); the same result is obtained, up to isomorphism, when using the “opposite” inclusions (which add a unit vector as new first row and column). In this note it is shown that passing to the colimit along both these families of inclusions simultaneously recovers the algebraic K-group K₁(R) = GL(R)/E(R) of R, giving an elementary description that does not involve elementary matrices explicitly. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics An elementary description of K₁(R) without elementary matrices Article published earlier |
| spellingShingle | An elementary description of K₁(R) without elementary matrices Hüttemann, T. Zhang, Z. |
| title | An elementary description of K₁(R) without elementary matrices |
| title_full | An elementary description of K₁(R) without elementary matrices |
| title_fullStr | An elementary description of K₁(R) without elementary matrices |
| title_full_unstemmed | An elementary description of K₁(R) without elementary matrices |
| title_short | An elementary description of K₁(R) without elementary matrices |
| title_sort | elementary description of k₁(r) without elementary matrices |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188554 |
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