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Transactions of the American Mathematical Society

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The class group of Dedekind domains


Author: C. R. Leedham-Green
Journal: Trans. Amer. Math. Soc. 163 (1972), 493-500
MSC: Primary 13G05
DOI: https://doi.org/10.1090/S0002-9947-1972-0292806-4
MathSciNet review: 0292806
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Abstract: A new proof is given of Claborn's theorem, namely that every abelian group is the class group of a Dedekind domain. A variation of the proof shows that the Dedekind domain can be constructed to be a quadratic extension of a principal ideal ring; a Dedekind domain is also constructed that is unrelated in a certain sense to any principal ideal ring.


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

  • [1] L. Claborn, Dedekind domains and rings of quotients, Pacific J. Math. 15 (1965), 59-64. MR 31 #2263. MR 0178005 (31:2263)
  • [2] -, Every abelian group is a class group, Pacific J. Math. 18 (1966), 219-222. MR 33 #4085. MR 0195889 (33:4085)
  • [3] E. Weiss, Algebraic number theory, McGraw-Hill, New York, 1963. MR 28 #3021. MR 0159805 (28:3021)
  • [4] O. Zariski and P. Samuel, Commutative algebra. Vol. 1, University Series in Higher Math., Van Nostrand, Princeton, N. J., 1958. MR 19, 833. MR 0090581 (19:833e)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0292806-4
Keywords: Class group, Dedekind domain
Article copyright: © Copyright 1972 American Mathematical Society

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