Is $\mathbb Q$ finitely generated as a $\mathbb Z$-module?
95240
Show that $({\mathbb{Q}},+)$ is not finitely generated using the Fundamental Theorem of Finitely Generated Abelian Groups.
153622
Are intermediate rings of finitely generated ring extensions also finitely generated?
28518
Hom of finitely generated modules over a noetherian ring
135611
Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
17304
Tensor product of two finitely-generated modules over a local ring is zero
34065
Submodule of free module over a p.i.d. is free even when the module is not finitely generated?
133019
Nilpotent elements in $\mathbb Z_n$
42810
Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
118073
Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
55050
How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
151993
Ring homomorphisms $\mathbb Z[x]\rightarrow \mathbb Q$
9806
$M$ finitely generated if submodule and quotient are finitely generated.
84114
Does there exist a surjective homomorphism from $(\mathbb R,+)$ to $(\mathbb Q,+)$ ?
104486
Ideal in $\mathbb Z[x]$ which is not two-generated
93681
Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
14259
If M+N and M$\cap$N are finitely generated modules, so are M and N.
64179
What is the difference between the standard representants of $\mathbb Z/q\mathbb Z$?