If $n$ elements generate a free module of rank $n$, are they necessarily linearly independent?
4790
Generators of a finitely generated free module over a commutative ring
3327
Height and minimal number of generators of an ideal
74974
When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module?
124864
A not free $\mathbb{Z}$-module
40996
Proving that free modules are flat (without appealing projective modules)
2719
Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?
39895
Showing a free abelian group is generated by its basis
133019
Nilpotent elements in $\mathbb Z_n$
99105
Are the functions $\sin^n(x)$ linearly independent?
101095
Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
50114
A question about direct sums and products of modules
103427
When is $\operatorname{Hom}_A(M,N)$ finitely generated?
8417
Natural $(R/I)$-module structure for an $R$-module $M$ annihilated by $I$
14259
If M+N and M$\cap$N are finitely generated modules, so are M and N.
55752
Prove that $n+1$ vectors in $\mathbb{R}^n$ cannot be linearly independent
79591
Exact Sequences of Modules and Rank
22629
rank of the free group: $\mathrm{rank} F_X=|X|$