Relative integral bases for quartic fields over quadratic subfields
โ Scribed by B. K. Spearman; K. S. Williams
- Publisher
- Akadmiai Kiad
- Year
- 1996
- Tongue
- English
- Weight
- 306 KB
- Volume
- 70
- Category
- Article
- ISSN
- 1588-2632
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Suppose that L#K are abelian extensions of the rationals Q with Galois groups (Zรq s Z) n and (Zรq r Z) m , respectively, q any prime number. It is proved that LรK 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
Focusing on a particular case, we will show that one can explicitly determine the quartic fields \(\mathbf{K}\) that have ideal class groups of exponent \(\leqslant 2\), provided that \(\mathbf{K} / \mathbf{Q}\) is not normal, provided that \(\mathbf{K}\) is a quadratic extension of a fixed imaginar