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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1317034
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Abstract | References | Similar Articles | Additional Information

Abstract: The image of the norm map from $R$ to $T$ (two rings of algebraic integers) is a multiplicative monoid $S$. We present conditions under which $R$ is a UFD if and only if $S$ has unique factorization into irreducible elements. From this we derive a bound for checking if $R$ is a UFD.


References [Enhancements On Off] (What's this?)

  • 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 (82b:12001)
  • 3. Władysław Narkiewicz, Elementary and analytic theory of algebraic numbers, 2nd ed., Springer-Verlag, Berlin, 1990. MR 1055830 (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: http://dx.doi.org/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
Article copyright: © Copyright 1996 American Mathematical Society