It is a sometimes useful lemma that if $\mathfrak{a}=(\alpha, \beta)$ is an ideal of a Dedekind domain $A$, then $\mathfrak{a}^n=(\alpha^n, \beta^n)$. Of course, this is easy to prove, but I'd like to be able to just give a reference. However, having looked in Neukirch's, Marcus' and Lang's books, I was not able to find one - do you know a reference for this fact?
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2Is a post here also a reference? I found this post, which should give what you want. – Dietrich Burde Apr 02 '22 at 18:38
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Hm, I would obviously have hoped for a textbook or something like that, but I guess it's better than nothing ... – mxian Apr 03 '22 at 14:30
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This is an exercise in Gilmer's Multiplicative Ideal Theory, in the section on Prüfer domains – Lukas Heger Apr 04 '22 at 14:32
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@Lukas Heger, thank you! Although the edition of the book I found in the library apparently didn't have any exercises, you get the result by combining two of the theorems proved there. – mxian Apr 06 '22 at 16:34