How to show that direct product of $\mathbb Z\times\mathbb Z\times\mathbb Z\times...$ is not projective as a $\mathbb Z$ module?
2719
Why isn't an infinite direct product of copies of $\Bbb Z$ a free module?
144122
A problem about an $R$-module that is both injective and projective.
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
93681
Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
55900
Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
128701
Are $\mathbb{Q}$ or $\mathbb{Z}$ flat modules?
141802
Prove that free modules are projective
108044
Isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent
36142
What is $\mathbb Z \oplus \mathbb Z / \langle (2,2) \rangle$ isomorphic to?
115876
$D_6 \cong D_3\times \mathbb Z_2$
124864
A not free $\mathbb{Z}$-module
67772
How to find $k$ such that $(\mathbb{Z} \times \mathbb{Z})/ \langle (m,n)\rangle \cong \mathbb{Z} \times \mathbb{Z}_k$
85193
direct product commutes with tensor product?
19884
The units of $\mathbb Z_4[x]$
2235
Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$
27472
Prove that $PSL(2,\mathbb{Z})$ is free product of $C_2$ and $C_3$
58717
Why isn't $\mathbb Z [\sqrt{pq}]$ a factorial domain