As we all know, the ring $\mathbb{Z}_p$ can be constructed as the projective limit of the rings $\mathbb{Z}/p^{n}\mathbb{Z}$.
Now is there any generalization such as the $p$-adic completions of a Dedekind Domain?
This might be said to be inspired by the general treatment of extensions of Dedekind Domains from the treatment of algebraic number fields.
In any case, thanks very much.
Is there a notion of *$p$-adic Dedekind Domains*?
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0In fact, at the beginning, I viewed this question as pretty abnormal, while now I realized that this question clarified the importance of Dedekind domains, and emphasized one of the proofs for the product formula which is the only one I know, i.e. via. unique factorization of prime ideals. – 2011-02-17