If $M\cong M_1\oplus M_2$ is a torsion-free module, does it follow that $M_1$ is a torsion-free module?
125058
Prove that direct sum of torsion module is torsion
2719
Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?
11319
Is $M=\{(x,|x|): x \in (-1, 1)\}$ not a differentiable manifold?
141149
Proof some module is direct sum by its submodules.
25609
Multiplicity of G-module
21466
$P$ is projective . Show that $P$ is a direct summand of a free $R-$ module
122559
Some questions on abelian category
142101
A direct product of projective modules which is not projective
142352
how to prove $G_1$ and $G_2$ aren't isomorphic?
82788
Direct summand of a free module
80302
A module $M$ whose submodules and factor modules are semisimple but not semisimple itself
137512
cup product in cohomology ring of a suspension
142699
Is $R/N(R)$ a faithfully flat $R$-module?
69384
Are the following modules free and/or isomorphic?
69398
Rank-nullity theorem for free $\mathbb Z$-modules
59687
Suppose $M$ is a finitely generated module over $R$ where $R$ is a Noetherian ring. Prove that $M$ is a noetherian module.
137029
Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.