Dedekind domain

A Dedekind domain is a CDR

A Dedekind domain is also a CDR, #m/thm/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 .

#state/tidy | #lang/en | #SemBr

Footnotes

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