On integral bases in relative quadratic extensions
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- by M. Daberkow and M. Pohst PDF
- Math. Comp. 65 (1996), 319-329 Request permission
Abstract:
Let $\mathcal F$ be an algebraic number field and $\mathcal E$ a quadratic extension with $\mathcal E=\mathcal F(\sqrt {\mu })$. We describe a minimal set of elements for generating the integral elements $o_{\mathcal E}$ of $\mathcal E$ as an $o_{\mathcal F}$ module. A consequence of this theoretical result is an algorithm for constructing such a set. The construction yields a simple procedure for computing an integral basis of $\mathcal E$ as well. In the last section, we present examples of relative integral bases which were computed with the new algorithm and also give some running times.References
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Additional Information
- M. Daberkow
- Affiliation: Technische Universität Berlin, Fachbereich 3, Sekr. Ma8-1, Straße des 17. Juni 136, 10623 Berlin, Germany
- Email: daberkow@math.tu-berlin.de
- M. Pohst
- Affiliation: Technische Universität Berlin, Fachbereich 3, Sekr. Ma8-1, Straße des 17. Juni 136, 10623 Berlin, Germany
- Email: pohst@math.tu-berlin.de
- Received by editor(s): June 17, 1994
- Received by editor(s) in revised form: November 29, 1994
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 319-329
- MSC (1991): Primary 11R04, 11R20, 11Y40
- DOI: https://doi.org/10.1090/S0025-5718-96-00686-2
- MathSciNet review: 1325866