On the Galois Structure of Units in Number Fields
β Scribed by Burns, D.
- Book ID
- 120101910
- Publisher
- Oxford University Press
- Year
- 1993
- Tongue
- English
- Weight
- 489 KB
- Volume
- s3-66
- Category
- Article
- ISSN
- 0024-6115
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π SIMILAR VOLUMES
Let p be an odd prime number and k a finite extension of Q p . Let K/k be a totally ramified elementary abelian Kummer extension of degree p 2 with Galois group G. We determine the isomorphism class of the ring of integers in K as an oG-module under some assumptions. The obtained results imply there
Let \(K\) be an algebraic number field and \(k\) be a proper subfield of \(K\). Then we have the relations between the relative degree \([K: k]\) and the increase of the rank of the unit groups. Especially, in the case of \(m\) th cyclotomic field \(Q\left(\zeta_{m}\right)\), we determine the number