Let $R$ be a commutative unital Noetherian ring such that, for every prime ideal $\mathfrak p\in\operatorname{Spec}(R)$, the local ring $R_{\mathfrak p}$ is a regular local ring. Let $R[t]$ be the [polynomial ring](/page/Polynomial%20Ring) in one variable over $R$, and let $i:R\to R[t]$ be the unital ring homomorphism sending each $r\in R$ to the constant polynomial $r$. Let $K_0$ and $K_1$ denote Quillen algebraic K-groups, and let $K_0(i)$ and $K_1(i)$ be the homomorphisms induced by functoriality, equivalently by extension of scalars along $i$. Then

\begin{align*} K_0(i):K_0(R)\to K_0(R[t]) \end{align*}

and

\begin{align*} K_1(i):K_1(R)\to K_1(R[t]) \end{align*}

are isomorphisms.