The class group of Dedekind domains
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- by C. R. Leedham-Green PDF
- Trans. Amer. Math. Soc. 163 (1972), 493-500 Request permission
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
- Luther Claborn, Dedekind domains and rings of quotients, Pacific J. Math. 15 (1965), 59–64. MR 178005
- Luther Claborn, Every abelian group is a class group, Pacific J. Math. 18 (1966), 219–222. MR 195889
- Edwin Weiss, Algebraic number theory, McGraw-Hill Book Co., Inc., New York-San Francisco-Toronto-London, 1963. MR 0159805
- Oscar Zariski and Pierre Samuel, Commutative algebra, Volume I, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, New Jersey, 1958. With the cooperation of I. S. Cohen. MR 0090581
Additional Information
- © Copyright 1972 American Mathematical Society
- 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