Fundamental theorem of ideal theory in number fields

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.

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