Example direct sum of injective modules is not injective
63541
Projective and injective modules; direct sums and products
98696
Is the exponential map ever not injective?
124864
A not free $\mathbb{Z}$-module
34065
Submodule of free module over a p.i.d. is free even when the module is not finitely generated?
73662
Example of non-flat modules
35953
Prove that a function is not injective
80211
Annihilator of quotient module M/IM
12474
Does an injective endomorphism of a finitely-generated free R-module have nonzero determinant?
149973
Showing the following coordinate rings are not isomorphic
153852
Example of modules that are projective but not free; torsion-free but not free
16275
Example of a simple module which does not occur in the regular module?
32127
Example where $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective
40996
Proving that free modules are flat (without appealing projective modules)
73898
Give an example of cochain map which is bijective?
93681
Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.