Dyadic Ramification and Quartic Number Fields
β Scribed by S.R. Ashford
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 677 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
This note presents a method that determines all power integral bases of a quartic number field by solving Thue equations of degrees 3 and 4. To this end, projective representations of the ring of integers by graded complete intersections are studied and a criterion for monogeneity in terms of projec
Let K be a field and K(Ξ±) be an extension field of K. If [K(Ξ±) : K] = 3, char K = 3, and the minimal polynomial of Ξ± over Kang (2000, Am. Math. Monthly, 107, 254-256) In this paper, we prove a similar result when [K(Ξ±) : K] = 4, char K = 2, and the minimal polynomial of Ξ± over K is T 4 -uT 2 -vT -w
In this paper we reduce the problem of solving index form equations in quartic number fields \(K\) to the resolution of a cubic equation \(F(u, v)=i\) and a corresponding system of quadratic equations \(Q_{1}(x, y, z)=u, Q_{2}(x, y, z)=v\), where \(F\) is a binary cubic form and \(Q_{1}, Q_{2}\) are
In this paper we determine all non-normal quartic CM-fields with relative class number two and all octic dihedral CM-fields with relative class number two: there are exactly 254 non-isomorphic non-normal quartic CM-fields with relative class number two and 95 non-isomorphic octic dihedral CM-fields