My question is pretty simple, I don't figure out why, if $I$ is a fractional ideal of $A$ (where $A$ is a Dedekind ring), $II^{-1}$ (at the moment I do not have proved that $II^{-1} = A$) should be an integral ideal of $A$ ? Actually, the fact that $\lambda II^{-1} \subset II^{-1}$ is pretty obvious, but I don't succeed to prove that $II^{-1}$ is a subgroup for $+$.
Someone could help me, please ?
Thank you !