Prove $\frac{k[x,y]}{I}$ and $k[x]$ are not isomorphic where $I=$.
1686
Show that quotient rings are not isomorphic
152104
How do I prove that $ij = k?$
108156
Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$
56171
Is $K(X)$ never algebraically closed?
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
79056
Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
9074
Example of non-isomorphic structures which are elementarily equivalent
94869
Show that $ \int_{k}^{2} \frac{1}{f(y)} =1$
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
1394
How do we know that $F = ma$, not $F = k \cdot ma$
94469
How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$?
14447
Direct proof that $\pi$ is not constructible
87101
Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$