In characteristic $p$, the field extension $k(X,Y)$ over $k(X^p,Y^p)$ is not simple
158353
If $F=K(u,v)$ with $u^p$,$v^p\in K$ and $[F:K]=p^2$, $\operatorname{char} K=p>0$, then $F$ is not a simple extension of $K$.
103654
A finite field extension that is not simple
92677
Infinite algebraic extension of a finite field
128550
Algebraic field extension and intermediate integral domain
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
158924
Example of composition of two normal field extensions which is not normal.
64068
Is every finite Galois extension of $\mathbb{Q}_p$ the completion of a number field at some valuation?
63390
Infinite algebraic extensions of $\mathbb{Q}$
78561
Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
103948
Minimal polynomial is invariant under field extensions
883
$K(u,v)$ is a simple extension of fields if $u$ is separable
7567
Degree of Field Extensions and $F(\alpha)$
115129
Constructing an explicit isomorphism between finite extensions of finite fields
74681
A finite extension with finitely many intermediate fields is simple
14270
Polynomial divisibility is unchanged by coeff. field extension
79450
For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
38489
Degree of the extension $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$