$\Bbb Z$ as a $\Bbb Z$-Module is not artinian but noetherian
74445
Noetherian and Artinian modules
77453
A zero-dimensional ring is Noetherian?
153852
Example of modules that are projective but not free; torsion-free but not free
112560
Simple Noetherian domain which is not a division ring
105103
Automorphism from $\Bbb Q$ to $\Bbb Q$
128861
If $M$ isn't Noetherian, $M$ has a submodule maximal with respect to being not finitely generated.
9562
Proving that surjective endomorphisms of Noetherian modules are isomorphisms and a semi-simple and noetherian module is artinian.
102938
$\Bbb F_2[X]$ modules with 8 elements
128732
$\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups
142101
A direct product of projective modules which is not projective
114640
Showing that an ideal is not a free $R-$module.
141124
Automorphisms of the ring $\Bbb Z[x]$ of polynomials with integer coefficients
80679
Principal ideal rings that are not integral domains
63338
Noncommutative failure of IBN: $\,R^n\cong R^m \Rightarrow n - m,$ ring $R$ with maximal ideal $I$ such that $R/I$ is not a division ring?
46717
If $M$ is a Noetherian $R$-module, then $R/\text{Ann}(M)$ is a Noetherian ring
122189
Show that $M[x]$ is a Noetherian $A[x]$-module.
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$