Let $R$ be an integral domain with field of fractions $K$, and let $I$ be a fractional ideal. If $I$ is projective then every $R$-linear maps $I\to R$ is multiplication by an element of $K$.
The three definitions of a projective module I have been playing with are: \begin{align*} (i)\; &\text{Every exact sequence } 0\to M\to N\to I\to 0\text{ splits}\\ (ii)\; &\text{The existence of a lifting homomorphism}\\ (iii)\;&I \text{ is the direct summand of a free module}. \end{align*} I am not sure what modules to use for $M$ and $N$, nor which definition should be used.