The ring of integers of an Abelian extension of an algebraic number field as a Galois module
β Scribed by S. V. Vostokov
- Publisher
- Springer US
- Year
- 1982
- Tongue
- English
- Weight
- 246 KB
- Volume
- 20
- Category
- Article
- ISSN
- 1573-8795
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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 p be a fixed odd prime number and k an imaginary abelian field containing a primitive p th root `p of unity. Let k Γk be the cyclotomic Z p -extension and LΓk the maximal unramified pro-p abelian extension. We put where E is the group of units of k . Let X=Gal(LΓk ) and Y=Gal(L & NΓk ), and let