An elementary description of \(K_1(R)\) without elementary matrices

• Date: 2020
• Main Authors: Hüttemann, T., Zhang, Z.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2020
• Subjects: \(K\)-theory; invertible matrix; elementary matrix; Primary 19B99; Secondary 16E20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1568
• Journal Title: Algebra and Discrete Mathematics

Let \(R\) be a ring with unit. Passing to the colimit with respect to the standard inclusions \(\mathrm{GL}(n,R) \to \mathrm{GL}(n+1,R)\) (which add a unit vector as new last row and column) yields, by definition, the stable linear group \(\mathrm{GL}(R)\); the same result is obtained, up to isomorp...