Galois: Why does $\{1,f,f^2\}$ correspond to $\mathbb{Q}(\omega)$?
Well but you are conflating $(f(\omega))^2=f(\omega)×f(\omega)=\omega×\omega$ with $f^2(\omega)=f(f(\omega))=f(\omega)=\omega$.
Galois: Why does $\{1,f,f^2\}$ correspond to $\mathbb{Q}(\omega)$?
Well but you are conflating $(f(\omega))^2=f(\omega)×f(\omega)=\omega×\omega$ with $f^2(\omega)=f(f(\omega))=f(\omega)=\omega$.