Exercise about field extensions
6869
The square roots of different primes are linearly independent over the field of rationals
63390
Infinite algebraic extensions of $\mathbb{Q}$
78222
Can any monomorphism of a subfield of a splitting field be extended to an automorphism?
19511
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
69935
Field extensions of finite degree and primitive elements
158525
Given a field, the field of algebraic elements over it in an algebraically closed field extension is again algebraically closed?
87467
Finding some missing subfields of a splitting field of $x^4-7$
18048
Easy criteria to determine isomorphism of fields?
128550
Algebraic field extension and intermediate integral domain
153589
Integral basis of an extension of number fields
151978
Splitting field of x^3-2 as a simple extension
127796
Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
131460
Example of finite field extension where root not separable
51770
Number of elements in a finite field extension for finite fields
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
16147
Generic Element of Compositum of Two Fields
103948
Minimal polynomial is invariant under field extensions