Let $R$ be a nonzero commutative unital ring, and let $\operatorname{Spec}(R)$ denote the set of prime ideals of $R$. Assume that every finitely generated projective $R$-module has constant rank in the following sense: for every finitely generated projective $R$-module $P$, there is a unique integer $r(P)\ge 0$ such that, for every prime ideal $\mathfrak p\in\operatorname{Spec}(R)$, the localized module $P_{\mathfrak p}$ is isomorphic to $R_{\mathfrak p}^{r(P)}$ as an $R_{\mathfrak p}$-module. Let $K_0(R)$ be the Grothendieck group of finitely generated projective $R$-modules, write $[P]\in K_0(R)$ for the class of a finitely generated projective module $P$, and let $\operatorname{rank}:K_0(R)\to \mathbb Z$ be the homomorphism induced by $[P]\mapsto r(P)$. Then the [group homomorphism](/page/Group%20Homomorphism) $s:\mathbb Z\to K_0(R)$ defined by $s(n)=n[R]$ is a section of $\operatorname{rank}$. Consequently, if $\widetilde K_0(R):=\ker(\operatorname{rank}:K_0(R)\to \mathbb Z)$, then there is an isomorphism of abelian groups $K_0(R)\cong \mathbb Z\oplus \widetilde K_0(R)$.