In this chapter we will deduce, with complete proofs, the most
important basic property of the ring of integers of an
algebraic number, namely that every nonzero ideals can be written
uniquely as products of prime ideals. After proving this fundamental
theorem, we will compute some examples using . The next chapter
will consist mostly of examples illustrating the substantial theory we
will have already developed, so hang in there!

**Subsections**

William Stein
2004-05-06