Definition:Dedekind Domain/Definition 5
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Definition
A Dedekind domain is a Noetherian domain $A$ of dimension $1$ such that for every maximal ideal $\mathfrak p$, the localization $A_{\mathfrak p}$ is a discrete valuation ring.
Also known as
A Dedekind domain is also known as a Dedekind ring.
Also see
- Results about Dedekind domains can be found here.
Sources
- 1969: M.F. Atiyah and I.G. MacDonald: Introduction to Commutative Algebra ... (previous): Chapter $9$: Discrete Valuation Rings and Dedekind Domains: $\S$ Dedekind domains