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...
Gespeichert in:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2020 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2020
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/188554 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-188554 |
|---|---|
| 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
An elementary description of K₁(R) without elementary matrices |
| spellingShingle |
An elementary description of K₁(R) without elementary matrices Hüttemann, T. Zhang, Z. |
| title_short |
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_sort |
elementary description of k₁(r) without elementary matrices |
| author |
Hüttemann, T. Zhang, Z. |
| author_facet |
Hüttemann, T. Zhang, Z. |
| publishDate |
2020 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/188554 |
| 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. |
| work_keys_str_mv |
AT huttemannt anelementarydescriptionofk1rwithoutelementarymatrices AT zhangz anelementarydescriptionofk1rwithoutelementarymatrices AT huttemannt elementarydescriptionofk1rwithoutelementarymatrices AT zhangz elementarydescriptionofk1rwithoutelementarymatrices |
| first_indexed |
2025-12-07T21:12:32Z |
| last_indexed |
2025-12-07T21:12:32Z |
| _version_ |
1850885487876636672 |