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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
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?)

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  • [2] -, Every abelian group is a class group, Pacific J. Math. 18 (1966), 219-222. MR 33 #4085. MR 0195889 (33:4085)
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Keywords: Class group, Dedekind domain
Article copyright: © Copyright 1972 American Mathematical Society

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