Degree of a field extension $F[x]/(g(x))$ over the field $F$
106284
Establishing a Basis for $F[x]/(f(x))$
19511
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
48093
Irreducible polynomial in field extension
78143
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
20218
Is this field extension finite?
17276
Number of points in the fibre and the degree of field extension
158525
Given a field, the field of algebraic elements over it in an algebraically closed field extension is again algebraically closed?
26999
How is the degree of the minimal polynomial related to the degree of a field extension?
155750
Why does $\mathbb{C}$ have transcendence degree $\mathfrak{c}$ over $\mathbb{Q}$?
142707
Intermediate fields of a finite field extension that is not separable
143219
If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$
78222
Can any monomorphism of a subfield of a splitting field be extended to an automorphism?
68753
Elements in finite field extensions
126127
A field extension of prime degree
28313
Intermediate ring between a field and an algebraic extension.
121301
What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?
60212
algebraic element over a field