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Dedekind domain

Dedekind domain noun: an integral domain in which every proper ideal factors into a product of prime ideals which is unique (up to permutations).

Noun

Dedekind domain (plural Dedekind domains)

  1. (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.
    • In this chapter we shall study several of the important classes of rings which contain the class of Dedekind domains.1971, Max D. Larsen, Paul J. McCarthy, Multiplicative Theory of Ideals, Elsevier (Academic Press), page 201
    Synonyms:
    Dedekind ring

Examples of Dedekind domain in a sentence

  • As we can see every principal ideal domain is a Dedekind domain.2007, Leonid Kurdachenko, Javier Otal, Igor Ya. Subbotin, Artinian Modules over Group Rings, Springer (Birkhäuser), page 55:
  • Let us recall some material about Dedekind domains from Chapters VIII and IX of Basic Algebra.2007, Anthony W. Knapp, Advanced Algebra, Springer (Birkhäuser), page 266:

Synonyms of Dedekind domain

Forms of Dedekind domain

pluralDedekind domains

Origin of Dedekind domain

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

Words formed from Dedekind domain

Questions about Dedekind domain

What does Dedekind domain mean?
Dedekind domain means an integral domain in which every proper ideal factors into a product of prime ideals which is unique (up to permutations).
How do you use Dedekind domain in a sentence?
As we can see every principal ideal domain is a Dedekind domain.
What part of speech is Dedekind domain?
Dedekind domain is a noun.
What is the plural of Dedekind domain?
The plural of Dedekind domain is Dedekind domains.

Words near Dedekind domain in the dictionary

  1. Dedeian
  2. Dedeians
  3. Dedekind
  4. Dedekind cut
  5. Dedekind cuts
  6. Dedekind domain
  7. Dedekind domains
  8. Dedekind ellipsoid
  9. Dedekind ellipsoids
  10. Dedekind ring
  11. Dedekind rings

Source and license

Adapted from Wiktionary: Dedekind domain (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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