Finite degree field extension is a simple extension iff there are only finitely many intermediate fields.
74681
A finite extension with finitely many intermediate fields is simple
16589
Field of fractions of integral extension is an algebraic extension
28803
Extension of degree 2 with characteristic not 2
19525
Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8
78561
Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
17276
Number of points in the fibre and the degree of field extension
111347
Finding an example of field extensions satisfying certain properties
140540
Infinite number of intermediate fields between K(u,v) and K
127796
Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
158590
Why is it that if $[L:K]$ is finite, then $[L:K]$ is algebraic?
126552
Number of subfields of finite field
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
68753
Elements in finite field extensions
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
137715
If $[L:K]$ is prime, show that $L/K$ is a simple extension.
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
78350
When does a finite ring become a finite field?