Example 10.55.5. Let $k$ be a field. Let $R = \{ f \in k[x] \mid f(0) = f(1)\}$, compare Example 10.27.4. In this case $K_0(R) \cong k^* \oplus \mathbf{Z}$, but $K'_0(R) = \mathbf{Z}$.

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