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Normsets and determination of unique factorization in rings of algebraic integers
Author(s):
Jim
Coykendall
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1727-1732.
MSC (1991):
Primary 11R04, 11R29;
Secondary 11Y40
MathSciNet review:
1317034
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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.
References:
- 1.
- J. W. S. Cassels and A. Frohlich, Algebraic Number Theory, Academic Press, London, 1967.
- 2.
- H. Cohn, Advanced Number Theory, Dover Publications, New York, 1980. MR 82b:12001
- 3.
- W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, Springer-Verlag/Polish Scientific Publishers, Warszawa, 1990. MR 91h:11107
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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:
10.1090/S0002-9939-96-03261-3
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
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