Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
57310
Prove $\mathbb{Z}$ is not a vector space over a field
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
98587
$\mathbb Z [X] / (X)$ isomorphic to $\mathbb Z[X] / (X+1)$ isomorphic to $\mathbb Z [X] / (X+2015)$
87160
Prove $\mathbb{Z}_3[x]/(x^2+1)$ and $\mathbb{Z}_3[x]/(x^2+x-1)$ are isomorphic.
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
33781
Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
981
If $n^c\in\mathbb N$ for every $n\in\mathbb N$, then $c$ is a non-negative integer?
66238
Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
99032
Prove that the additive group of $\mathbb{Z}[x]$ is isomorphic to the group of positive rational numbers under multiplication.
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
5906
All group homomorphism from $ \mathbb{Z} _m $ to $\mathbb{Z}_n $
147574
Prove of a finite cyclic group of order $n$ is isomorphic tto $(\mathbb Z_n,+)$.
5699
The number of ring homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$
23879
If $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$