Projective module over a PID is free?
34065
Submodule of free module over a p.i.d. is free even when the module is not finitely generated?
124864
A not free $\mathbb{Z}$-module
55764
Algebraic closure of $\mathbb F_p$
4790
Generators of a finitely generated free module over a commutative ring
142699
Is $R/N(R)$ a faithfully flat $R$-module?
117211
Infinite linear independent family in a finitely generated $A$-module
70218
Flat not projective, projective not free
28324
Inverse image of the sheaf associated to a module
142101
A direct product of projective modules which is not projective
145879
$R$ is PID, so $R/I$ is PID, and application on $\mathbb{Z}$ and $\mathbb{N}$
70872
Isomorphism of quotient modules implies isomorphism of submodules?
141149
Proof some module is direct sum by its submodules.
145758
Are submodules of finitely generated free modules always free?
122387
Is a stably free module always free?
117208
Smith Normal Form for PIDs
102879
$\operatorname{Ext}$ and injectives, respectively projectives
140314
A module as an external direct product of the kernel and image of an idempotent function