TY  - JOUR
KW  - Algebra - monogén mez?
KW  -  monogenic fields
KW  -  számmez?k kompozitjai
KW  -  cubic Thue egyenlet
AV  - restricted
N2  - 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.
ID  - acta66324
UR  - http://acta.bibl.u-szeged.hu/66324/
SP  - 413
A1  -  Gaál István
A1  -  Remete László
TI  - Power integral bases in cubic and quartic extensions of real quadratic fields
SN  - 2064-8316
VL  - 85
IS  - 3-4
EP  - 429
JF  - Acta scientiarum mathematicarum
N1  - Bibliogr.: p. 428-429.
Y1  - 2019///
ER  -