On relative integral bases for cyclic quartic fields
β Scribed by John A Hymo; Charles J Parry
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 379 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Suppose that L#K are abelian extensions of the rationals Q with Galois groups (ZΓq s Z) n and (ZΓq r Z) m , respectively, q any prime number. It is proved that LΓK 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
We develop an algorithm for computing all generators of relative power integral bases in quartic extensions K of number fields M. For this purpose we use the main ideas of our previously derived algorithm for solving index form equations in quartic fields (I. Gaa l, A.
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 Ξ for L is known. We reduce our problem to the problem of finding the generator of a principal ideal in the pth