Criteria for local freeness of a module
117211
Infinite linear independent family in a finitely generated $A$-module
40996
Proving that free modules are flat (without appealing projective modules)
114773
counterexamples on modules
73825
Every $R$-module is a quotient of a free module
22529
The support of a non finitely generated module
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
128493
Given a commutative ring $R$ and an epimorphism of free modules $R^m \to R^n$ is then $m \geq n$?
141477
Decomposition of finitely generated graded modules over PID
124864
A not free $\mathbb{Z}$-module
5246
Is noetherianity a local property?
114640
Showing that an ideal is not a free $R-$module.
120637
Is there a unique cyclic submodule for every factor dividing the order of a cyclic module?
156005
Pullback of locally free sheaves is locally free
148828
Submodule of a free module
29359
Localisation isomorphic to a quotient of polynomial ring
52554
Showing that localization is an exact functor
74445
Noetherian and Artinian modules