Why is $ℤ[X]/(X^2-1)$ not isomorphic with $ℤ×ℤ$?
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
151047
a non trivial example: $G/H$ is isomorphic to $G$
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
68014
Prove that $\mathfrak{su}(2)$ is not isomorphic to $\mathfrak{sl}(2,\mathbb R)$
92599
Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$
108123
Why is $\mathbb{C}[x,y]/(y^2 - x^3 + 1)$ normal?
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
108633
Why $f^{-1}(f(A)) \not= A$
69384
Are the following modules free and/or isomorphic?
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
14830
A transformation of F[x]
49444
Why isn't $e^{2\pi xi}=1$ true for all $x$?
29359
Localisation isomorphic to a quotient of polynomial ring
93118
How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?
56234
Isomorphism $f$ preserves the order of an element?
78118
Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?