Dedekind domain

A Dedekind domain is an integral domain \(R\) in which every nonzero ideal \(I\) factors as a product \(I=\mfp_1\cdots\mfp_n\) of nonzero prime ideals, with \(n\geq 0\) and the empty product equal to \(R\), and this factorization is unique up to the order of the factors.