Show that $E/F$ is Galois extension
6824
Extensions of degree two are Galois Extensions.
101371
show that $f^{(3)}(c) \ge 3$ for $c\in(-1,1)$
121301
What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?
53432
What is the algebraic closure of $\mathbb F_q$?
59108
Book for field and galois theory.
86877
Let $F$ be a Galois extension over $\mathbb{Q}$ with $[F:\mathbb{Q}]=2^n$, then all elements in $F$ are constructible
120943
Galois field extension and number of intermediate fields
103148
Show Galois group of $f(t) = t^5 - 3$ over $\mathbb Q$ is solvable
31142
Why does $K \leadsto K(X)$ preserve the degree of field extensions?
48780
How t show $f=g$ almost everywhere
132423
Non trivial valuation over a finite extension $F/\mathbb{Q}_p$ is equivalent to the one induced by $v_p$
74681
A finite extension with finitely many intermediate fields is simple
98968
$X$ is algebraic over $E$
31961
Given fields $M/E/F$, why does $[M:F] = [M:E][E:F]$?
147069
Intersection of field extensions
102553
How to show that $f(z) = f(i)$
1060
Minimal polynomial of intermediate extensions under Galois extensions.