Show that $α^2$ is algebraic over $K$
60348
How do I prove $F(a)=F(a^2)?$
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
39082
Proving $x^\alpha-\alpha x \le 1- \alpha $
24551
How to prove that the sum and product of two algebraic numbers is algebraic?
100725
Let $a$ be an algebraic number, prove that $ia$ is also algebraic
15626
Relations of a~b iff b = ak^2
98968
$X$ is algebraic over $E$
146047
Proving that $\cos(2\pi/n)$ is algebraic
133561
show that if $K$ is a field then $K[x]$ is principal
66946
show that $(i+k)! > i!k!$ algebraically
157031
Express $x^8-x$ as a product of irreducibles in $\Bbb Z_2[x]$
105170
About product of $k$ commutators
79450
For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
116588
All polynomial parametric curves in $k^2$ are contained in affine algebraic varieties
9140
Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
35959
irreducibility of a polynomial over $\mathbb{F}_2$