An elementary description of K₁(R) without elementary matrices

• Published in: Algebra and Discrete Mathematics
• Date: 2020
• Main Authors: Hüttemann, T., Zhang, Z.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188554
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...