Exercise 8.1.4 (Galois correspondence)

Question

Prove the first half of Lemma 8.1.2(i).

Hassaan Naeem · Accepted Answer

extbf{Solution:}
We assume that $L_1 \subseteq L_2$ and let $\phi \in Gal(M:L_2)$. Then we have that $\phi(\alpha) = \alpha \ \forall \alpha \in L_2$.
Hence we have that $\phi(\alpha) = \alpha \ \forall \alpha \in L_1$, hence $\phi \in Gal(M:L_1)$. Therefore $Gal(M:L_1) \supseteq Gal(M:L_2)$.

Exercise 8.1.4 (Galois correspondence)

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Exercise 8.1.4 (Galois correspondence)

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