Elliptic curves and Dedekind domains

Rosen, Michael

doi:10.1090/S0002-9939-1976-0417190-3

Elliptic curves and Dedekind domains
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by Michael Rosen

Proc. Amer. Math. Soc. 57 (1976), 197-201

DOI: https://doi.org/10.1090/S0002-9939-1976-0417190-3

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Abstract:

Some results are obtained on the group of rational points on elliptic curves over infinite algebraic number fields. A certain naturally defined class of Dedekind domains, elliptic Dedekind domains, are described and it is shown that every countable abelian group can be realized as the class group of an elliptic Dedekind domain.

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