$R/(x) \cong R/(x^2)$ implies $(x)=(x^2)$
70658
Isomorphism between quotient modules
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
104688
How can I prove that $x-{x^2\over2}<\ln(1+x)$
52088
Isomorphism of an endomorphism ring, how can $R\cong R^2$?
8374
How to prove that $R/I \otimes_R M \cong M / IM$
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
48537
If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
84189
Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
106911
Square root of $-1$ in the ring $\mathbb{R}[x]/\langle(x^2+1)^2\rangle$
53575
Describe $R=\mathbb{Z}[X]/(X^2-3,2X+4)$
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$
87397
Show that $a^2 \bmod b = (a \bmod b)^2 \bmod b$
147564
Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?
29452
Divisor in $\mathbb{C}[X]$ $\implies$ divisor in $\mathbb{R}[X]$?