If $\mathbb{Q}(\zeta)=\mathbb{Q}(\eta), [\mathbb{Q}(f(\zeta)):\mathbb(Q)]=[\mathbb{Q}(f(\eta)):\mathbb(Q)]$ must $\mathbb(Q)(\zeta)=\mathbb(Q)(\eta)$?

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Compositum of normal extensions is normal

Published on 10 Apr 2026 - 20:47

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If $\mathbb{Q}(\zeta)=\mathbb{Q}(\eta), [\mathbb{Q}(f(\zeta)):\mathbb(Q)]=[\mathbb{Q}(f(\eta)):\mathbb(Q)]$ must $\mathbb(Q)(\zeta)=\mathbb(Q)(\eta)$?

Compositum of normal extensions is normal

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