Normsets and determination of unique factorization in rings of algebraic integers
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- by Jim Coykendall PDF
- Proc. Amer. Math. Soc. 124 (1996), 1727-1732 Request permission
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
- J. W. S. Cassels and A. Frohlich, Algebraic Number Theory, Academic Press, London, 1967.
- Harvey Cohn, Advanced number theory, Dover Books on Advanced Mathematics, Dover Publications, Inc., New York, 1980. Reprint of A second course in number theory, 1962. MR 594936
- Władysław Narkiewicz, Elementary and analytic theory of algebraic numbers, 2nd ed., Springer-Verlag, Berlin; PWN—Polish Scientific Publishers, Warsaw, 1990. MR 1055830
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
- Received by editor(s): March 21, 1994
- Received by editor(s) in revised form: December 29, 1994
- Communicated by: William W. Adams
- © Copyright 1996 American Mathematical Society
- 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