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.
The maximal ideal of an integrally closed Noetherian local domain of Krull dimension one is principal. Hence every such local ring is a discrete valuation ring.
Articles by others on the same topic
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.