Let be $F\subset E$ finite field extension, prove that $F\subset E$ is separable iff $\Omega_{E/F}=0$. ($\Rightarrow$) it's ok, but for ($\Leftarrow$) i've got some problems. I supposed $F\subset E$ is not separable, then $\exists a\in E$ s.t. $p_a(x)$ minimum polinomial is not separable. Then I've got that $\Omega_{F[a]/F}\neq 0$. It's true that $\Omega_{F[a]/F}\subset \Omega_{E/F}$? Is that true in general?
2026-03-24 23:44:29.1774395869
Kähler Differential Of Submodules
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