Is $\bar{\mathbb{Q}}/\mathbb{Q}$ finitely generated field extension?
97004
Algebraic closure not even finitely generated over base field
63390
Infinite algebraic extensions of $\mathbb{Q}$
146617
A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
140938
Finitely generated projective module
147069
Intersection of field extensions
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
34740
Do finite algebraically closed fields exist?
74681
A finite extension with finitely many intermediate fields is simple
16163
Show $\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a simple extension field of $\mathbb{Q}$.
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
155266
Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?
134840
Generators and relations for $\text{PSL}(2, \mathbb{F}_q)$
80538
Fields extensions over isomorphic fields of different degrees
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
109039
Does this "extension property" for polynomial rings satisfy a universal property?