Free module finite generated with a submodule not finite generated.
4624
Example of a finitely generated module with submodules that are not finitely generated
28518
Hom of finitely generated modules over a noetherian ring
153622
Are intermediate rings of finitely generated ring extensions also finitely generated?
145933
Localization commutes with Hom for finitely-generated modules
46258
Example of Artinian module that is not Noetherian
142101
A direct product of projective modules which is not projective
124864
A not free $\mathbb{Z}$-module
104486
Ideal in $\mathbb Z[x]$ which is not two-generated
114640
Showing that an ideal is not a free $R-$module.
148828
Submodule of a free module
37570
$M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences
120637
Is there a unique cyclic submodule for every factor dividing the order of a cyclic module?
23735
Divisible module which is not injective
17304
Tensor product of two finitely-generated modules over a local ring is zero
141149
Proof some module is direct sum by its submodules.
8417
Natural $(R/I)$-module structure for an $R$-module $M$ annihilated by $I$
39652
Quotient of free module