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- W2977734265 abstract "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). In this note it is shown that passing to the colimit along both these families of inclusions simultaneously recovers the algebraic $K$-group $K_1(R) = GL(R)/E(R)$ of~$R$, giving an elementary description that does not involve elementary matrices explicitly." @default.
- W2977734265 created "2019-10-10" @default.
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- W2977734265 date "2019-09-09" @default.
- W2977734265 modified "2023-09-27" @default.
- W2977734265 title "An elementary description of $K_1(R)$ without elementary matrices" @default.
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