Do we have $K(\beta)=K(\beta^2)$ for field extension of odd degree?
22430
Equal simple field extensions?
155245
root of an odd degree polynomial
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
118610
Are all extensions of finite fields cyclic?
127796
Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
82328
Constructing a Galois extension field with Galois group $S_n$
94579
$\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
10111
Prove or disprove that Q[√2] is a field
143219
If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
111347
Finding an example of field extensions satisfying certain properties
67157
Example of an non-normal inseparable field extension
14918
Degree of splitting field of $X^n-1$ over some finite field
6984
Inverting $a+b\sqrt{2}$ in the field $\Bbb Q(\sqrt{2})$
36034
Degree of splitting field less than n!
73669
Totally real Galois extension of given degree
8164
Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$?
128550
Algebraic field extension and intermediate integral domain