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...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2019
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| Sorozat: | Acta scientiarum mathematicarum
85 No. 3-4 |
| Kulcsszavak: | Algebra - monogén mező, monogenic fields, számmezők kompozitjai, cubic Thue egyenlet, Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-018-080-z |
| Online Access: | http://acta.bibl.u-szeged.hu/66324 |
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| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Gaál István | |
| 245 | 1 | 0 | |a Power integral bases in cubic and quartic extensions of real quadratic fields |h [elektronikus dokumentum] / |c Gaál István |
| 260 | |a Bolyai Institute, University of Szeged |b Szeged |c 2019 | ||
| 300 | |a 413-429 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 85 No. 3-4 | |
| 520 | 3 | |a 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. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Algebra - monogén mező, monogenic fields, számmezők kompozitjai, cubic Thue egyenlet, Matematika | ||
| 700 | 0 | 1 | |a Remete László |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/66324/1/math_085_numb_003-004_413-429.pdf |z Dokumentum-elérés |