whitehead theorem for k1 of a ring

Let \(R\) be a ring.
Then \(K_1(R) = \mathrm{Gl}(R)/\mathrm{E}(R)\)

see:

1. K1 of a ring
   
2. \(\mathrm{Gl}(R)\) is the infinite general linear group
   
3. \(\mathrm{E}(r)\) is the infinite elementary linear group
   

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