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 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.