Fundamental theorem of ideal theory in number fields

In ideal 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.

References

• Keith Conrad, Ideal factorization
• Hilbert, D. The Theory of Algebraic Number Fields. Trans. by Iain T. Adamson. Springer Verlag. ISBN 3-540-62779-0.