Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Properties of the normset relating to the class group
HTML articles powered by AMS MathViewer

by Jim Coykendall PDF
Proc. Amer. Math. Soc. 124 (1996), 3587-3593 Request permission

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
  • R. T. Bumby, Irreducible integers in Galois extensions, Pacific J. Math. 22 (1967), 221–229. MR 213322, DOI 10.2140/pjm.1967.22.221
  • R. T. Bumby and E. C. Dade, Remark on a problem of Niven and Zuckerman, Pacific J. Math. 22 (1967), 15–18. MR 211982, DOI 10.2140/pjm.1967.22.15
  • 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
  • J. Coykendall, Normsets and determination of unique factorization in rings of algebraic integers, Proc. Amer. Math. Soc. 124 (1996), 1727–1732.
  • Georges Gras, Sur les $l$-classes d’idĂ©aux dans les extensions cycliques relatives de degrĂ© premier $l$. I, II, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 3, 1–48; ibid. 23 (1973), no. 4, 1–44 (French, with English summary). MR 360519, DOI 10.5802/aif.471
  • Marie-Nicole Gras, MĂ©thodes et algorithmes pour le calcul numĂ©rique du nombre de classes et des unitĂ©s des extensions cubiques cycliques de $\textbf {Q}$, J. Reine Angew. Math. 277 (1975), 89–116 (French). MR 389845, DOI 10.1515/crll.1975.277.89
  • Marshall Hall Jr., The theory of groups, Chelsea Publishing Co., New York, 1976. Reprinting of the 1968 edition. MR 0414669
  • WĹ‚adysĹ‚aw Narkiewicz, Elementary and analytic theory of algebraic numbers, 2nd ed., Springer-Verlag, Berlin; PWN—Polish Scientific Publishers, Warsaw, 1990. MR 1055830
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11R04, 11R29, 11Y40
  • Retrieve articles in all journals with MSC (1991): 11R04, 11R29, 11Y40
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
  • Received by editor(s): December 21, 1994
  • Received by editor(s) in revised form: March 27, 1995
  • Communicated by: William W. Adams
  • © Copyright 1996 American Mathematical Society
  • 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