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Aug 3, 2021 at 9:21 comment added Matthieu Romagny @Piotr thank you! In fact I think there are many specific cases where one can prove that F is surjective. The general case still eludes me (and I'm not even sure if surjectivity holds).
Aug 3, 2021 at 9:18 comment added Matthieu Romagny @Wojowu yes, I mean an epimorphism of unitary commutative rings.
Jul 31, 2021 at 20:44 comment added Piotr Achinger P.S. I remember that in a normal ring $R$, the kernel of $d:R\to \Omega^1_R$ equals $R^p$, so in this case the answer to your question should be yes.
Jul 31, 2021 at 20:33 comment added Piotr Achinger Interpreting derivations $R\to M$ as homomorphisms $R\to R\oplus M\cdot\varepsilon$, the condition implies that $\Omega^1_R=0$. I don’t know if this observation is useful.
Jul 31, 2021 at 20:24 comment added Wojowu I take it "epimorphism" is meant in categorical sense? Some authors use it for surjective ring homomorphisms.
Jul 31, 2021 at 20:20 history asked Matthieu Romagny CC BY-SA 4.0