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On the Structure of (OK/I)×

✍ Scribed by Claus Mazanti Sorensen

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
195 KB
Volume
86
Category
Article
ISSN
0022-314X

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✦ Synopsis

In this paper we investigate the structure of the unit group of O K ÂI where K is a global number field, and I is a nonzero ideal in the ring of integers O K . 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 p n . We obtain an explicit decomposition of (O K Âp n ) _ in cyclic groups for almost all primes p, namely those lying above a rational prime p satisfying p>e where e=e(p, Z) is the ramification index. In particular we obtain the structure of (O K Âp n ) _ for all unramified p.

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