Normal integral bases of ∞ -ramified abelian extensions of totally real number fields
✍ Scribed by Fuminori Kawamoto; Yoshitaka Odai
- Publisher
- Vandenhoeck & Ruprecht
- Year
- 2002
- Tongue
- German
- Weight
- 830 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0025-5858
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📜 SIMILAR VOLUMES
Let K=Q(-m) be a real quadratic number field. In this article, we find a necessary and sufficient condition for K to admit an unramified quadratic extension with a normal integral basis distinct from K(-&1), provided that the prime 2 splits neither in KÂQ nor in Q(-&m)ÂQ, in terms of a congruence sa
Suppose that L#K are abelian extensions of the rationals Q with Galois groups (ZÂq s Z) n and (ZÂq r Z) m , respectively, q any prime number. It is proved that LÂK has a relative integral basis under certain simple conditions. In particular, [L : K] q s or q s +1 (according to q is odd or even) is e
Let k be a real abelian number field with Galois group 2 and p an odd prime number. Denote by k the cyclotomic Z p -extension of k with Galois group 1 and by k n the nth layer of k Âk. Assume that the order of 2 is prime to p and that p splits completely in kÂQ. In this article, we describe the orde
Let L be a cyclic number field of prime degree p. In this paper we study how to compute efficiently a normal integral basis for L, if there is at least one, assuming that an integral basis Γ for L is known. We reduce our problem to the problem of finding the generator of a principal ideal in the pth