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Properties of the normset relating
to the class group


Author: Jim Coykendall
Journal: Proc. Amer. Math. Soc. 124 (1996), 3587-3593
MSC (1991): Primary 11R04, 11R29; Secondary 11Y40
DOI: https://doi.org/10.1090/S0002-9939-96-03387-4
MathSciNet review: 1328342
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Abstract: In a recent paper by the author the normset and its multiplicative structure was studied. In that paper it was shown that under certain conditions (including Galois) that a normset has unique factorization if and only if its corresponding ring of integers has unique factorization. In this paper we shall examine some of the properties of a normset and describe what it says about the class group of the corresponding ring of integers.


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

  • 1. R.T. Bumby, Irreducible integers in Galois extensions, Pacific J. Math. 22 (2) (1967), 221-229. MR 35:4186
  • 2. R.T Bumby and E.C. Dade, Remark on a problem of Niven and Zuckerman, Pacific J. Math. 22 (1) (1967), 15-18. MR 35:2857
  • 3. H. Cohn, Advanced Number Theory, Dover Publications, New York, 1980. MR 82b:12001
  • 4. J. Coykendall, Normsets and determination of unique factorization in rings of algebraic integers, Proc. Amer. Math. Soc. 124 (1996), 1727-1732. CMP 95:08
  • 5. G. Gras, Sur les l-classes d'ideaux dans les extensions cycliques relatives de degre premier l, Annales de l'Institut Fourier 23 (3) (1973), 1-48; and 23 (4) (1973), 1-43. MR 50:12967
  • 6. -, Méthodes et algorithmes pour le calcul numérique du nombre de classes et des unités des extensions cubiques cycliques de $\mathbf {Q}$, J. Reine Angew. Math. 277 (1975), 89-116. MR 52:10675
  • 7. M. Hall, The theory of groups, Chelsea Publishing Co., New York, 1976. MR 54:2765
  • 8. 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, North Dakota State University, Fargo, North Dakota 58105-5075

DOI: https://doi.org/10.1090/S0002-9939-96-03387-4
Received by editor(s): December 21, 1994
Received by editor(s) in revised form: March 27, 1995
Communicated by: William W. Adams
Article copyright: © Copyright 1996 American Mathematical Society

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