𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Computing Power Integral Bases in Quartic Relative Extensions

✍ Scribed by István Gaál; Michael Pohst

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
157 KB
Volume
85
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ Synopsis

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.

📜 SIMILAR VOLUMES

Power Bases in Dihedral Quartic Fields
Power Bases in Dihedral Quartic Fields
✍ Anthony C Kable 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 119 KB

A quartic number field, L, is called dihedral if the normal closure, N, of L satisfies Gal(NÂQ)$D 8 . We investigate whether or not the ring of integers of such a quartic field has a power basis. When the quadratic subfield of L is imaginary, the problem is completely solved. When it is real, the sa

Existence of Integral Bases for Relative
Existence of Integral Bases for Relative Extensions ofn-Cyclic Number Fields
✍ XianKe Zhang; FuHua Xu 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 303 KB

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