Format:
1 Online-Ressource (208p)
ISBN:
9781461200857
,
9780817642716
Note:
One of the classical problems in algebraie number theory, going back, among others, to K. Hensel [He08] and H. Hasse [Ha63], is to deeide if an algebraie number field K of degree n has a power integral basis, that is, an integral basis n 1 oftype {I, Ci, ... , Ci - }. This is equivalent to 7l,K being monogenie, that is ofthe form 7l,[ Ci]. The main purpose of this book is to deseribe algorithms for determining generators Ci of power integral bases. This problem is equivalent to solving the eorresponding index form equations. It is important to emphasize that in addition to providing the reader with some efficient algorithms for eomputing generators of power integral bases, the other goal in this work is to show the development of constructive (algorithmic) methods for solving diophantine equations, whieh has eome about as a eonsequenee of a systematic study of index form equations. This has a signifieant impact on our investigations of power integral bases. Many of these methods ean also be applied to solving other types of diophantine equations
Language:
English
Keywords:
Algebraischer Körper
;
Basis
;
Diophantische Gleichung
DOI:
10.1007/978-1-4612-0085-7
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