Unique factorization of ideals in a Dedekind domain
= Unique factorization of ideals in a Dedekind domain
Every nonzero proper <ideal> of a <Dedekind domain> has a unique factorization, up to reordering, as a finite product of positive powers of distinct nonzero <prime ideals>. The unit <ideal> is the empty product. This is distinct from unique factorization of elements.