A Dedekind domain is a Noetherian integrally closed domain of Krull dimension one. Equivalently, every localization at a nonzero prime ideal is a discrete valuation ring.
A **Dedekind domain** is a specific type of ring that plays a significant role in number theory, algebraic geometry, and algebraic number theory. A Dedekind domain is defined as an integral domain that satisfies certain properties. Here are the key characteristics of a Dedekind domain: 1. **Noetherian**: The ring is Noetherian, meaning that every ideal is finitely generated.
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