I was going through the notes, where these two examples on Dedekind domain I couldn't prove. I don't know much about Dedekind domains. Can anyone answer or at least provide some materials and hints so that I can think of an approach to proof.
(Example 1.2.1) Suppose $R$ is a Dedekind domain which is not a Principal ideal domain (PID). If $I$ is an ideal of $R$ that is not principal, then $I$ is not isomorphic to $R$ but $I_m$ $\cong$ $R_m$ for all maximal ideals $m$ of $R$.
(Example 1.2.2) Suppose $R$ is a Dedekind domain that is not a PID. Let $I$ be an ideal that is not principal. Then $I_m$ is one generated for all $m$ in max $R$.