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Yes, these are calledIf you add the hypothesis that Prüfer rings, see Bourbaki, Commutative Algebra VII, §2$D$ is noetherian, Exercise 12. This exercise gives 14 (!) equivalentthen this is one of the characterizations of theseDedekind rings...

Yes, these are called Prüfer rings, see Bourbaki, Commutative Algebra VII, §2, Exercise 12. This exercise gives 14 (!) equivalent characterizations of these rings...

If you add the hypothesis that $D$ is noetherian, then this is one of the characterizations of Dedekind rings.

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abx
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Yes, these are called Prüfer rings, see Bourbaki, Commutative Algebra VII, §2, Exercise 12. This exercise gives 14 (!) equivalent characterizations of these rings...