Definition:Dedekind Domain/Definition 5

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

• Equivalence of Definitions of Dedekind Domain

• 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