Prove that $\alpha$ is algebraic over $\mathbb Q$.
158590
Why is it that if $[L:K]$ is finite, then $[L:K]$ is algebraic?
68430
Proving the countability of algebraic numbers
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
21972
How to show that $\sqrt{2}+\sqrt{3}$ is algebraic?
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
97583
Let $\alpha, \beta, \gamma$ be cardinals, $\beta \leq \gamma$, prove $\alpha ^{\beta}\le \alpha ^{\gamma}$
73713
Prove that $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$ is Galois over $\mathbb{Q}$ is Galois and determine the Galois group
81895
A generalisation of the fundamental theorem of algebra
150605
Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$
7567
Degree of Field Extensions and $F(\alpha)$
55764
Algebraic closure of $\mathbb F_p$
134896
Enlightening proof that the algebraic numbers form a field
155125
Every ordered field has a subfield isomorphic to $\mathbb Q$?
122759
Show $2+\alpha$ is a primitive root of $\mathbb{F}_{25}$.
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.
13147
Proof verification - Minimal polynomial of $\alpha$ has integer coef.s iff its an alg. integer
34998
How to prove that $\mathbb{Q}$ ( the rationals) is a countable set