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Normal Bases and Zp-Extensions

✍ Scribed by F. Kawamoto; K. Komatsu

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
458 KB
Volume
163
Category
Article
ISSN
0021-8693

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πŸ“œ SIMILAR VOLUMES

On a Normal Integral Basis Problem over
On a Normal Integral Basis Problem over Cyclotomic Zp-extensions, II
✍ Humio Ichimura πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 283 KB

Let p be an odd prime number, K an imaginary abelian field with z p 2 K Γ‚ ; and K 1 =K the cyclotomic Z p -extension with its nth layer K n : In the previous paper, we showed that for any n and any unramified cyclic extension L=K n of degree p; LK nΓΎ1 =K nΓΎ1 does have a normal integral basis (NIB) e

Cyclotomic Units in Zp-Extensions
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✍ Dirk Hachenberger πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 114 KB

w3E is called normal over F if its conjugates under the Galois group of E/F form an F-basis of E. For the theory of normal bases we refer to [Ha1].

On Capitulation of S-Ideals in Zp-Extens
On Capitulation of S-Ideals in Zp-Extensions
✍ Hiroki Sumida πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 167 KB

Let k be a finite extension of Q and p a prime number. Let K be a Z p -extension of k and S the set of all prime ideals in k which are ramified in K. We denote by A$ the p-Sylow subgroup of the S-divisor class group of K. We give a criterion for A$ =0 which can be applied for general Z p -extensions