Dedekind domain

A Dedekind domain is a CDR

A Dedekind domain is also a CDR, ring i.e. given ideals we have¹

Proof

The forward direction already holds in general (vide ^D1).
Since Fractional ideals of a Dedekind domain form an abelian group, if then so and .

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Footnotes

1. 2022. Algebraic number theory course notes, ¶1.39, p. 20 ↩