Factorization problems in semigroups.
Factorizations of distinct lengths in algebraic number fields
Fermat quotient of cyclotomic units
Finite abelian groups and factorization problems
Finite abelian groups and factorization problems. II
Finiteness theorems for factorizations.
Formulations algébriques de la conjecture de Leopoldt et applications
Frobenius groups and integral bases.
Fundamental units for orders in certain cubic number fields.
Fundamental units for orders of unit rank 1 and generated by a unit
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...
Fundamental units from the perperiod of a generalized Jacobi-Perron algorithm.
Fundamental units in a family of cubic fields
Let be the maximal order of the cubic field generated by a zero of for , . We prove that is a fundamental pair of units for , if
Fundamental units in a parametric family of not totally real quintic number fields
In this article we compute fundamental units for a family of number fields generated by a parametric polynomial of degree 5 with signature and Galois group .
Généralisation de la théorie des fractions continues
Généralisation d'une famille de Shanks
Global quadratic units and Hecke algebras.
Global units and ideal class groups.
Große Faktoren in der Klassengruppe algebraischer Zahlkörper
Groupe des classes de l'algèbre d'un groupe métacyclique.
Groupe des unités pour des extensions diédrales complexes de degré sur
Le but de cet article est de montrer qu’un ensemble quelconque de quatre racines des polynômes quintiques exhibés par . Darmon forme sous certaines conditions un système fondamental d’unités de la fermeture normale du corps où .