Power integral bases in cubic and quartic extensions of real quadratic fields

Investigations of monogenity and power integral bases were recently extended from the absolute case (over Q) to the relative case (over algebraic number fields). Formerly, in the relative case we only succeeded in calculating generators of power integral bases when the ground field is an imaginary q...

Teljes leírás

Elmentve itt :
Bibliográfiai részletek
Szerzők: Gaál István
Remete László
Dokumentumtípus: Cikk
Megjelent: 2019
Sorozat:Acta scientiarum mathematicarum 85 No. 3-4
Kulcsszavak:Algebra - monogén mező, monogenic fields, számmezők kompozitjai, cubic Thue egyenlet
doi:10.14232/actasm-018-080-z

Online Access:http://acta.bibl.u-szeged.hu/66324
Leíró adatok
Tartalmi kivonat:Investigations of monogenity and power integral bases were recently extended from the absolute case (over Q) to the relative case (over algebraic number fields). Formerly, in the relative case we only succeeded in calculating generators of power integral bases when the ground field is an imaginary quadratic field. This is the first case when we consider monogenity in the more difficult case, in extensions of real quadratic fields. We give efficient algorithms for calculating generators of power integral bases in cubic and quartic extensions of real quadratic fields, more exactly in composites of cubic and quartic fields with real quadratic fields. In case the quartic field is totally complex, we present an especially simple algorithm. We illustrate our method with two detailed examples.
Terjedelem/Fizikai jellemzők:413-429
ISSN:2064-8316