A Dedekind domain is an integral domain in which every nonzero proper ideal factors into a product of prime ideals, and an integral domain $R$ is called almost Dedekind whenever $R_m$ is Dedekind domain for every maximal ideal $m$ of $R $. It is well known that a Dedekind domain is *noetherian* and so it's maximal spectrum is *noetherian* space as a subspace of Zariski topology.
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An almost Dedekind domain with

noetherianmaximal spectrum is a Dedekind domain.