# Dedekind domain

## Contents

## English[edit]

### Etymology[edit]

Named after Richard Dedekind (1831–1916), German mathematician.

### Noun[edit]

**Dedekind domain** (*plural* **Dedekind domains**)

- (algebra, ring theory) An integral domain in which every proper ideal factors into a product of prime ideals which is unique (up to permutations).
*It can be proved that a***Dedekind domain**(as defined above) is equivalent to an integral domain in which every proper fractional ideal is invertible.