Remark on a problem of Niven and Zuckerman

Richard Thomas Bumby and Everett C. Dade

Vol. 22 (1967), No. 1, 15–18

DOI: 10.2140/pjm.1967.22.15

Abstract

An integer of an algebraic number field K is called irreducible if it has no proper integer divisors in K. Every integer of K can be written as a product of irreducible integers, usually in many different ways. Various problems have been inspired by this lack of unique factorization. This paper studies the question: When are the irreducible integers of K determined by their norms? Attention is confined to the case in which K is a quadratic field. With this assumption it is possible to give a complete answer in terms of the ideal class group of K and the nature of the units of K.

Mathematical Subject Classification

Primary: 10.66

Milestones

Received: 22 August 1966

Published: 1 July 1967