In number theory, the fundamental theorem of ideal theory in number fields states that every nonzero proper ideal in the ring of integers of a number field admits unique factorization into a product of nonzero prime ideals. In other words, every ring of integers of a number field is a Dedekind domain.
References Keith Conrad, Ideal factorization Hilbert, D. (20 August 1998). The Theory of Algebraic Number Fields. Trans. by Iain T. Adamson. Springer Verlag. ISBN 3-540-62779-0.