M is finitely generated but $\ker(f)\subset M$ is not.
4624
Example of a finitely generated module with submodules that are not finitely generated
1394
How do we know that $F = ma$, not $F = k \cdot ma$
42652
Must $k$-subalgebra of $k[x]$ be finitely generated?
4383
Finitely generated monoids - how to show that there is not first order set axiomatizing them.
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
151467
An infinite generating set of a finite dimensional vector space contains a basis
128489
Linearly independent elements are less than generators in a module.
93029
Prove that when $d$ is in $\mathbb{Q} \setminus\mathbb{Z}$, $\mathbb{Z}[\sqrt{d}]$ is not a finitely generated abelian group.
107389
Show that the vector space of real functions is not finitely spanned
104851
A finite field cannot be an ordered field.
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
68672
Commutator subgroup of rank-2 free group is not finitely generated.
107207
$A\subseteq B\subseteq C$ ring extensions, $A\subseteq C$ finite/finitely-generated $\Rightarrow$ $A\subseteq B$ finite/finitely-generated?
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
132382
Showing a set is nowhere dense in $C([0,1])$
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
24988
Prove there exists $m > 2010$ such that $f(m)$ is not prime