Prove that $(\mathbb{Z},+)$ and $(\mathbb{Q},+)$ are not isomorphic.
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
73713
Prove that $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$ is Galois over $\mathbb{Q}$ is Galois and determine the Galois group
86542
Group of positive rationals under multiplication not isomorphic to group of rationals
125604
Proof that $\mathbb{Z}$ has no zero divisors
98587
$\mathbb Z [X] / (X)$ isomorphic to $\mathbb Z[X] / (X+1)$ isomorphic to $\mathbb Z [X] / (X+2015)$
135611
Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
41035
Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
61084
Examples of non-isomorphic fields with isomorphic group of units and additive group structure
42810
Is $(\mathbb{Q},+)$ isomorphic to $(\mathbb{Q}^n,+)$?
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
7607
How to prove that $\mathbb{Q}$ is not the intersection of a countable collection of open sets.
40400
Finding an isomorphism between $\mathbb{Z}[i]/(7)$ and $\mathbb{Z}[\sqrt{-2}]/(7)$
47914
Prove $\Bbb{Z}_{100} \times \Bbb{Z}_{10}$ is not isomorphic to $\Bbb{Z}_{1000}$
82046
prove that this double transpose $T''$ it's not injective.
87160
Prove $\mathbb{Z}_3[x]/(x^2+1)$ and $\mathbb{Z}_3[x]/(x^2+x-1)$ are isomorphic.
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
62635
Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.