Noun
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.
Also, a Dedekind domain is a UFD if and only if its ideal class group is trivial. Source: Internet
There is a version of unique prime factorization for the ideals of a Dedekind domain (a type of ring important in number theory ). Source: Internet