$\mathbb{Z}[x_{1},\dots,x_{n}]/I$ is a field therefore it's finite
29635
Fields finitely generated as $\mathbb Z$-algebras are finite?
104486
Ideal in $\mathbb Z[x]$ which is not two-generated
8623
Finite subgroups of the multiplicative group of a field are cyclic
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
151786
Proving that there is no ideal $I$ in $\mathbb{Z}[t]$ such that $\mathbb{Z}[t]/I \cong \mathbb{Q}$
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
16643
A slick proof that a field which is finitely generated as a ring is finite
93681
Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
78350
When does a finite ring become a finite field?
69046
Proof of $\mathbb{Q}$ is not cyclic
41895
Show $\text{Hom}_{Ab}(A,\mathbb{Q}) = \{0\}$ for finite $A$
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
20218
Is this field extension finite?
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
8434
Order of $\mathbb{Z}[i]/(1+i)$
151928
How to prove that $N\setminus A$ is finite?