Diophantine relationships between algebraic number fields
β Scribed by Harold N. Shapiro; Alexandra Shlapentokh
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 402 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0010-3640
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let \(K\) be an algebraic number field and \(k\) be a proper subfield of \(K\). Then we have the relations between the relative degree \([K: k]\) and the increase of the rank of the unit groups. Especially, in the case of \(m\) th cyclotomic field \(Q\left(\zeta_{m}\right)\), we determine the number
We prove that any order O of any algebraic number field K is a reduction ring. Rather than showing the axioms for a reduction ring hold, we start from scratch by well-ordering O, defining a division algorithm, and demonstrating how to use it in a Buchberger algorithm which computes a GrΓΆbner basis g