Fundamental units for orders of unit rank 1 and generated by a unit

• Autorzy: Stéphane R. Louboutin
• Języki publikacji: EN

Abstrakty

EN

Let ε be an algebraic unit for which the rank of the group of units of the order ℤ[ε] is equal to 1. Assume that ε is not a complex root of unity. It is natural to wonder whether ε is a fundamental unit of this order. It turns out that the answer is in general yes, and that a fundamental unit of this order can be explicitly given (as an explicit polynomial in ε) in the rare cases when the answer is no. This paper is a self-contained exposition of the solution to this problem, solution which was up to now scattered in many papers in the literature.

Kategorie tematyczne

• 11R16: Cubic and quartic extensions
• 11R27: Units and factorization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2016
• Tom: 108
• Numer: 1
• Strony: 173-189

Daty

wydano

2016

Twórcy

autor

Stéphane R. Louboutin

• Aix Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France

Identyfikatory

DOI

10.4064/bc108-0-14