Let $\Pi$ be a complete SCR polyhedral complex in $N_{\mathbb{R}}$ and let ${\mathcal{X}}_{\Pi}$ be the associated toric scheme over $S$. The correspondence $\psi\mapsto D_{\psi}$ is an isomorphism between the group of H-lattice functions on $\Pi$ and the group of $\mathbb{T}$-Cartier divisors on ${\mathcal{X}}_{\Pi}$. Moreover, if $\psi_{1}$ and $\psi_{2}$ are two H-lattice functions on $\Pi$, then the divisors $D_{\psi_{1}}$ and $D_{\psi_{2}}$ are rationally equivalent if and only if $\psi_{1}-\psi_{2}$ is affine.