If $E/F$ is algebraic and every $f\in F[X]$ has a root in $E$, why is $E$ algebraically closed?
19511
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
113175
Why is the algebraic closure of a finite field countable?
53432
What is the algebraic closure of $\mathbb F_q$?
97004
Algebraic closure not even finitely generated over base field
31961
Given fields $M/E/F$, why does $[M:F] = [M:E][E:F]$?
85096
Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.
66293
$der(\{x\})$ is closed and $x\in der(der(A))$
65054
How is $e^z$ the only function that is entire with the property $f'(z) = f(z)$ and $f(0) = 1$
127796
Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
123219
What is multiplicative group $\bar{\mathbb{F}}_p^*$ for algebraic closure $\bar{\mathbb{F}}_p$ of $\mathbb{F}_p$ where $p$ is prime?
4000
If every polynomial of degree 2 is reducible then $K$ is algebraically closed?
43431
Show that $F+G$ is closed when $G$ a closed subspace of normed space $E$ and $F$ a finite dimensional subspace of $E$.
118874
If $v$ is algebraic over $K(u)$, for some $u\in F$, and $v $ is transcendental over $K$, then $u$ is algebraic over $K(v)$
41810
Should all polynomial functions from F to F (F is a field) have coefficients in F?
135641
Algebraic independence of exponentials
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
115502
Analogue of the Cantor-Bernstein-Schroeder theorem for general algebraic structures