In this chapter we will prove the main structure theorem for the group
of units of the ring of integers of a number field. The answer is
remarkably simple: if has real and complex embeddings,
then
where is the finite cyclic group of roots
of unity in . Examples will follow on Thursday (application:
the solutions to Pell's equation
, for squarefree,
form a free abelian group of rank ).

**Subsections**

William Stein
2004-05-06