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Factorization in Krull monoids with infinite class group

Florian Kainrath (1999)

Colloquium Mathematicae

Let H be a Krull monoid with infinite class group and such that each divisor class of H contains a prime divisor. We show that for each finite set L of integers ≥2 there exists some h ∈ H such that the following are equivalent: (i) h has a representation $h = u_{1} \cdot . . . \cdot u_{k}$ for some irreducible elements $u_{i}$ , (ii) k ∈ L.

Factorization of natural numbers in algebraic number fields

A. Geroldinger (1991)

Acta Arithmetica

Factorization problems in class number two

Franz Halter-Koch (1993)

Colloquium Mathematicae

Factorization problems in semigroups.

A. Geroldinger, G. Lettl (1990)

Semigroup forum

Factorizations of distinct lengths in algebraic number fields

Jan Śliwa (1976)

Acta Arithmetica

Fermat quotient of cyclotomic units

Tsutomu Shimada (1996)

Acta Arithmetica

Finite abelian groups and factorization problems

W. Narkiewicz (1979)

Colloquium Mathematicae

Finite abelian groups and factorization problems. II

W. Narkiewicz, J. Śliwa (1982)

Colloquium Mathematicae

Finiteness theorems for factorizations.

F. Halter-Koch (1992)

Semigroup forum

Formulations algébriques de la conjecture de Leopoldt et applications

Thong Nguyen-Quang-Do (1981/1982)

Groupe de travail d'analyse ultramétrique

Frobenius groups and integral bases.

Leon R. McCulloh (1971)

Journal für die reine und angewandte Mathematik

Fundamental units for orders in certain cubic number fields.

Emery Thomas (1979)

Journal für die reine und angewandte Mathematik

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

Stéphane R. Louboutin (2016)

Banach Center Publications

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.

Leon Bernstein (1974)

Journal für die reine und angewandte Mathematik

Fundamental units in a family of cubic fields

Veikko Ennola (2004)

Journal de Théorie des Nombres de Bordeaux

Let $𝒪$ be the maximal order of the cubic field generated by a zero $ε$ of $x^{3} + (ℓ - 1) x^{2} - ℓ x - 1$ for $ℓ \in ℤ$ , $ℓ \geq 3$ . We prove that $ε, ε - 1$ is a fundamental pair of units for $𝒪$ , if $[𝒪 : ℤ [ε]] \leq ℓ / 3 .$

Fundamental units in a parametric family of not totally real quintic number fields

Andreas M. Schöpp (2006)

Journal de Théorie des Nombres de Bordeaux

In this article we compute fundamental units for a family of number fields generated by a parametric polynomial of degree 5 with signature $(1, 2)$ and Galois group $D_{5}$ .

Currently displaying 1 – 16 of 16

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