Using totally ramified prime to find the degree of extension of cyclotomic field.
137711
Alternative proof that $[\Bbb{Q}(\zeta_n) : \Bbb{Q} ]= \varphi(n)$ uses circular reasoning?
6824
Extensions of degree two are Galois Extensions.
111347
Finding an example of field extensions satisfying certain properties
64068
Is every finite Galois extension of $\mathbb{Q}_p$ the completion of a number field at some valuation?
19525
Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8
80538
Fields extensions over isomorphic fields of different degrees
137373
Real Cyclic Extensions of $\mathbb Q$ of given degree
122952
Degree of extension is equal to linear combination of prime factor multiplicities with prime factor index coefficients in Dedekind domains
23153
$\bmod p\!:\ x^2\equiv 1\iff x\equiv \pm1\ $ for prime $p$
147069
Intersection of field extensions
127796
Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
17276
Number of points in the fibre and the degree of field extension
76813
The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
92677
Infinite algebraic extension of a finite field
146446
Infinite Degree Algebraic Field Extensions
68790
Do we have $K(\beta)=K(\beta^2)$ for field extension of odd degree?