Dedekind Domain

Noetherian domain where ideals factor uniquely into primes — the natural home of algebraic number theory and of NTRU-like cryptography.

Specifications & Metrics

type

Rings & Fields

originator

Richard Dedekind

Core Principles & Analysis

• A Noetherian domain in which every nonzero proper ideal factors into prime ideals — ideals factor uniquely even when elements do not.
• Being a Dedekind domain is a local property among Noetherian domains: it holds iff it holds after localizing at every maximal ideal.
• The ring of integers of a number field is always a Dedekind domain.

Sources

• Wikipedia: Dedekind domain