Why $\mathbb{Q}$ is not a projective $\mathbb{Z}$-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.
17978
Isomorphism classes of $\mathbb{Z}[i]$ modules.
69046
Proof of $\mathbb{Q}$ is not cyclic
118073
Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
155750
Why does $\mathbb{C}$ have transcendence degree $\mathfrak{c}$ over $\mathbb{Q}$?
104562
Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
93681
Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
66020
What is $\mathbb Z[[t]]$? What are the double brackets?
141802
Prove that free modules are projective
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
78118
Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
121246
Projective modules and $\hom(P,\cdot)$
124864
A not free $\mathbb{Z}$-module
74974
When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module?
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.