Normsets and determination
of unique factorization
in rings of algebraic integers
Author:
Jim Coykendall
Journal:
Proc. Amer. Math. Soc. 124 (1996), 1727-1732
MSC (1991):
Primary 11R04, 11R29; Secondary 11Y40
DOI:
https://doi.org/10.1090/S0002-9939-96-03261-3
MathSciNet review:
1317034
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Abstract | References | Similar Articles | Additional Information
Abstract: The image of the norm map from 
to 
(two rings of algebraic integers) is a multiplicative monoid 
. We present conditions under which 
is a UFD if and only if 
has unique factorization into irreducible elements. From this we derive a bound for checking if 
is a UFD.
- 1. J. W. S. Cassels and A. Frohlich, Algebraic Number Theory, Academic Press, London, 1967.
- 2. Harvey Cohn, Advanced number theory, Dover Publications, Inc., New York, 1980. Reprint of A second course in number theory, 1962; Dover Books on Advanced Mathematics. MR 594936
- 3. Władysław Narkiewicz, Elementary and analytic theory of algebraic numbers, 2nd ed., Springer-Verlag, Berlin; PWN—Polish Scientific Publishers, Warsaw, 1990. MR 1055830
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Additional Information
Jim Coykendall
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853
Address at time of publication:
Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
Email:
jimbob@math.cornell.edu, jbc4@lehigh.edu
DOI:
https://doi.org/10.1090/S0002-9939-96-03261-3
Keywords:
Normsets,
Galois (extension),
norm factorization field (extension),
Minkowski bound
Received by editor(s):
March 21, 1994
Received by editor(s) in revised form:
December 29, 1994
Communicated by:
William W. Adams
Article copyright:
© Copyright 1996
American Mathematical Society
