B4.6

Number Fields
Part II, 2004

Let KK be a finite extension of Q\mathbb{Q}, and O\mathcal{O} the ring of integers of KK. Write an essay outlining the proof that every non-zero ideal of O\mathcal{O} can be written as a product of non-zero prime ideals, and that this factorisation is unique up to the order of the factors.