$K[X,Y]/(XY-1)$ not isomorphic to $K[T]$
1686
Show that quotient rings are not isomorphic
130367
Proof that $K\otimes_F L$ is not noetherian
92599
Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
70688
How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
158502
Showing $\sin(\bar{z})$ is not analytic at any point of $\mathbb{C}$
58329
Show that $y_1$ and $y_2$ are not Linearly Independent
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
18160
How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
8694
$A_4$ is not isomorphic to $D_6$
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
118903
The sup norm on $C[0,1]$ is not equivalent to another one, induced by some inner product
87101
Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
33781
Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?