Displaying similar documents to “The Artin conjecture for Q-algebras.”

A simple characterization of principal ideal domains

Clifford S. Queen (1993)

Acta Arithmetica

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1. Introduction. In this note we give necessary and sufficient conditions for an integral domain to be a principal ideal domain. Curiously, these conditions are similar to those that characterize Euclidean domains. In Section 2 we establish notation, discuss related results and prove our theorem. Finally, in Section 3 we give two nontrivial applications to real quadratic number fields.

On the prime density of Lucas sequences

Pieter Moree (1996)

Journal de théorie des nombres de Bordeaux

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The density of primes dividing at least one term of the Lucas sequence L n ( P ) n = 0 ∞ , defined by L 0 ( P ) = 2 , L 1 ( P ) = P and L n ( P ) = P L n - 1 ( P ) + L n - 2 ( P ) for n ≥ 2 , with P an arbitrary integer, is determined.

On the 2-primary part of K₂ of rings of integers in certain quadratic number fields

A. Vazzana (1997)

Acta Arithmetica

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1. Introduction. For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of K ₂ E . For quadratic fields whose discriminant has arbitrarily many prime divisors, the formulas are less explicit. In this paper we will study fields of the form ℚ ( √ ( p ₁ . . . p k ) ) , where the primes p i are all congruent to 1 mod 8. We will prove a theorem conjectured by Conner and Hurrelbrink which examines under what conditions the 4-rank of K ₂ E is zero for such fields. In the course...