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Existence of Integral Bases for Relative Extensions ofn-Cyclic Number Fields

✍ Scribed by XianKe Zhang; FuHua Xu

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 303 KB
Volume: 60
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0131

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✦ Synopsis

Suppose that L#K are abelian extensions of the rationals Q with Galois groups (ZÂq s Z) n and (ZÂq r Z) m , respectively, q any prime number. It is proved that LÂK has a relative integral basis under certain simple conditions. In particular, [L : K] q s or q s +1 (according to q is odd or even) is enough. The relative discriminant D(LÂK) is also computed explicitly and is proved to be generated by a rational square under a (necessary and sufficient) condition.

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✍ Vincenzo Acciaro; Claus Fieker 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 237 KB

Let L be a cyclic number field of prime degree p. In this paper we study how to compute efficiently a normal integral basis for L, if there is at least one, assuming that an integral basis Γ for L is known. We reduce our problem to the problem of finding the generator of a principal ideal in the pth