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So there are easy examples for algebraic closures that have index two and infinite index: C $\mathbb{C}$ over R $\mathbb{R}$ and the algebraic numbers over Q. $\mathbb{Q}$. What about the other indices?

EDIT: Of course Cl(Q) != C. $\overline{\mathbb{Q}} \neq \mathbb{C}$. I don't know what I was thinking.

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So there are easy examples for algebraic closures that have index two and infinite index: C over R and C the algebraic numbers over Q. What about the other indices?

EDIT: Of course Cl(Q) != C. I don't know what I was thinking.

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# Examples of algebraic closures of finite index

So there are easy examples for algebraic closures that have index two and infinite index: C over R and C over Q. What about the other indices?