Dedekind domain

== English == === Etymology === Named after German mathematician Richard Dedekind (1831–1916). === 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). ==== Usage notes ==== For a list of equivalent definitions, see Dedekind domain on Wikipedia.Wikipedia ==== Synonyms ==== (integral domain whose prime ideals factorise uniquely): Dedekind ring ==== Hypernyms ==== (integral domain whose prime ideals factorise uniquely): Noetherian domain ==== Derived terms ==== almost Dedekind domain ==== Translations ==== === Further reading === Ideal class group on Wikipedia.Wikipedia Unique factorization domain on Wikipedia.Wikipedia Dedekind ring on Encyclopedia of Mathematics Dedekind Ring on Wolfram MathWorld