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On the Discriminants of the Powers of an Algebraic Integer

Published online by Cambridge University Press:  22 May 2019

Stéphane R. Louboutin*
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, I2M, Marseille, France Email: [email protected]

Abstract

For $\unicode[STIX]{x1D6FC}$ an algebraic integer of any degree $n\geqslant 2$, it is known that the discriminants of the orders $\mathbb{Z}[\unicode[STIX]{x1D6FC}^{k}]$ go to infinity as $k$ goes to infinity. We give a short proof of this result.

Type
Article
Copyright
© Canadian Mathematical Society 2019

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