On the minimum index of a cyclic quartic field
β Scribed by Toru Nakahara
- Book ID
- 112496495
- Publisher
- Springer
- Year
- 1987
- Tongue
- English
- Weight
- 175 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0003-889X
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π SIMILAR VOLUMES
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
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