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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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.


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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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