Intermediate field of $\Bbb Q(\alpha)$ and $\Bbb Q$
56439
$f \in K[X]$ of degree $n$ with Galois group $S_n$, why are there no non-trivial intermediate fields of $K \subset K(a)$ with $a$ a root of $f$?
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
157074
The elements in the composite field $FK$
76900
$\Bbb Q$-linear is equivalent to additive
126127
A field extension of prime degree
118310
How to find $\operatorname{Gal}(S/\mathbb{Q})$
42213
Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
27021
Show that $Q[\sqrt3]$ is a field
145726
For a subfield $K$ of $\Bbb C$ with $K\nsubseteq \Bbb R$, show $K$ is dense in $\Bbb C$.
58416
Valuations on $\Bbb Q(t)$
1060
Minimal polynomial of intermediate extensions under Galois extensions.
80538
Fields extensions over isomorphic fields of different degrees
125568
Construction of $p^n$ field
7567
Degree of Field Extensions and $F(\alpha)$
74681
A finite extension with finitely many intermediate fields is simple
80295
Field extensions and algebraic/transcendental elements