On the Structure of (OK/I)× Original Research Article

In this paper we investigate the structure of the unit group of OK/I where K is a global number field, and I is a nonzero ideal in the ring of integers OK. The case I=0 is given by the Dirichlet unit theorem. By the Chinese remainder theorem we may assume that I is a prime power imagen. We obtain an explicit decomposition of (OK/imagen)× in cyclic groups for almost all primes image, namely those lying above a rational prime p satisfying p>e where e=e(image, image) is the ramification index. In particular we obtain the structure of (OK/imagen)× for all unramified image.