Vol. 22, No. 1, 1967

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Remark on a problem of Niven and Zuckerman

Richard Thomas Bumby and Everett C. Dade

Vol. 22 (1967), No. 1, 15–18

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
Received: 22 August 1966
Published: 1 July 1967
Richard Thomas Bumby
Everett C. Dade
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green St.
Urbana IL 61801-2975
United States