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Named after German mathematician Richard Dedekind (1831–1916).
- (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.
- 1971, Max D. Larsen, Paul J. McCarthy, Multiplicative Theory of Ideals, Elsevier (Academic Press), page 201,
- In this chapter we shall study several of the important classes of rings which contain the class of Dedekind domains.
- 2007, Leonid Kurdachenko, Javier Otal, Igor Ya. Subbotin, Artinian Modules over Group Rings, Springer (Birkhäuser), page 55,
- As we can see every principal ideal domain is a Dedekind domain.
- 2007, Anthony W. Knapp, Advanced Algebra, Springer (Birkhäuser), page 266,
- Let us recall some material about Dedekind domains from Chapters VIII and IX of Basic Algebra. A Dedekind domain is a Noetherian integral domain that is integrally closed and has the property that every nonzero prime ideal is maximal. Any Dedekind domain has unique factorization for its ideals.
- For a list of equivalent definitions, see Dedekind domain#Alternative definitions on Wikipedia.Wikipedia
- (integral domain whose prime ideals factorise uniquely): Dedekind ring
- (integral domain whose prime ideals factorise uniquely): Noetherian domain
integral domain whose prime ideals factorise uniquely