A free $A$-module $M$ which is also finitely-generated.
127044
Prove that a finitely-generated free module has a finite basis
134991
Commutative non Noetherian rings in which all maximal ideals are finitely generated
14259
If M+N and M$\cap$N are finitely generated modules, so are M and N.
34065
Submodule of free module over a p.i.d. is free even when the module is not finitely generated?
95930
Finitely generated modules over a Noetherian ring are Noetherian
153852
Example of modules that are projective but not free; torsion-free but not free
141802
Prove that free modules are projective
134294
A (not necessarily unitary) $R$ module $M$ splits into $B\oplus C$ where $B$ is unitary and $RC=\{0\}$.
116955
Showing the existence of a certain kind of extension of a finitely generated algebra
23392
The annihilator of a module is an ideal
28518
Hom of finitely generated modules over a noetherian ring
102072
Simple $M_n(D)$-module with $D$ a division ring
141477
Decomposition of finitely generated graded modules over PID
69384
Are the following modules free and/or isomorphic?
152730
Example of a finitely generated faithful torsion module over a commutative ring
75641
Is there a (f.g., free) module isomorphic to a quotient of itself?
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module