In
abstract algebra, a
Dedekind domain or
Dedekind ring, named after
Richard Dedekind, is an
integral domain in which every nonzero
proper ideal factors into a product of
prime ideals. It can be shown that such a factorization is then necessarily unique up to the order of the factors. There are at least three other characterizations of Dedekind domains that are sometimes taken as the definition: see below.