# An elementary description of $K_1(R)$ without elementary matrices

10 Oct 2019 Huettemann Thomas Zhang Zuhong

Let $R$ be a ring with unit. Passing to the colimit with respect to the standard inclusions $GL(n,R) \to GL(n+1,R)$ (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)... (read more)

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• K-THEORY AND HOMOLOGY