๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Finding Normal Integral Bases of Cyclic Number Fields of Prime Degree

โœ Scribed by Vincenzo Acciaro; Claus Fieker

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
237 KB
Volume
30
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 ฮ“ for L is known. We reduce our problem to the problem of finding the generator of a principal ideal in the pth cyclotomic field.

๐Ÿ“œ SIMILAR VOLUMES

Existence of Integral Bases for Relative
Existence of Integral Bases for Relative Extensions ofn-Cyclic Number Fields
โœ XianKe Zhang; FuHua Xu ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 303 KB

Suppose that L#K are abelian extensions of the rationals Q with Galois groups (Zร‚q s Z) n and (Zร‚q r Z) m , respectively, q any prime number. It is proved that Lร‚K 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

Unramified Quadratic Extensions of Real
Unramified Quadratic Extensions of Real Quadratic Fields, Normal Integral Bases, and 2-AdicL-Functions
โœ A Srivastav; S Venkataraman ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 320 KB

Let K=Q(-m) be a real quadratic number field. In this article, we find a necessary and sufficient condition for K to admit an unramified quadratic extension with a normal integral basis distinct from K(-&1), provided that the prime 2 splits neither in Kร‚Q nor in Q(-&m)ร‚Q, in terms of a congruence sa