Let $\displaystyle R$be a Dedekind domain with the quotient field $\displaystyle K$.
If $\displaystyle M$ and $\displaystyle N$ are projective $\displaystyle R$-module of rank $\displaystyle 1$ and if $\displaystyle f:M\to N$ is $\displaystyle R$-linear then $\displaystyle f$ is given by multiplication by some $\displaystyle x \in K$.