Prove there does not exist any epimorphism of $(\mathbb{Q}, +)$ onto $(\mathbb{Z}, +)$.
98731
Show that there is no epimorphism from ($\mathbb{Q}$, +) to ($\mathbb{Z}$, +)
7607
How to prove that $\mathbb{Q}$ is not the intersection of a countable collection of open sets.
62224
Need help with proof for Dedekind cuts on $\mathbb{Q}^+$
34177
Prove that $\mathbb{R}^2\setminus\mathbb{Q}^2$ is connected without path connectedness
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
77620
Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
55050
How to show that $\mathbb{Q}(i,\sqrt[4]{1+i} )$ is not contained in any cyclotomic extension of $\mathbb{Q}(i)$?
157597
Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
234
No continuous function switches $\mathbb{Q}$ and the irrationals
150605
Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$
63390
Infinite algebraic extensions of $\mathbb{Q}$
86015
$\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
146980
Zero divisors of $\mathbb{Z}×\mathbb{Z}×\mathbb{Z}$
104562
Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
149849
Let $F$ be a field and $f: \mathbb{Z} \to F$ be a ring epimorphism.
143831
Showing $\mathbb{Q}$ is homeomorphic to $\mathbb{Q}^2$