$k$ is algebraically closed in $K$, and $lK=L$ , but $l$ is not algebraically closed in $L$.
111347
Finding an example of field extensions satisfying certain properties
156679
$K[X,Y]/(XY-1)$ not isomorphic to $K[T]$
77791
Proving an inclusion related to algebraic sets and interpreting it
33370
Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
53432
What is the algebraic closure of $\mathbb F_q$?
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
107281
Proof of Existence of Algebraic Closure: Too simple to be true?
74792
$(X,\tau)$ needs to be $T_1$ in order to guarantee that $A'$ is closed?
64502
On the meaning of being algebraically closed
21114
$S=\{(n,{1\over n}):n\in\mathbb{N}\}$ is closed in $X$?
34740
Do finite algebraically closed fields exist?
71935
Let $k$ be a natural number . Then $3k+1$ , $4k+1$ and $6k+1$ cannot all be square numbers.
123903
If $E/F$ is algebraic and every $f\in F[X]$ has a root in $E$, why is $E$ algebraically closed?
126897
Showing the set $A+B$ is closed.
7607
How to prove that $\mathbb{Q}$ is not the intersection of a countable collection of open sets.
153100
A counterexample to "$k\mid n$ if and only if $k\mid n^2$"
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?