Does $R/I \cong R$ implies $I=0$?
75641
Is there a (f.g., free) module isomorphic to a quotient of itself?
35188
Counterexample: $G \times K \cong H \times K \implies G \cong H$
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
125763
If $\mathrm{tr}(A)=0$, then we have $A=BC-CB?$
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
142699
Is $R/N(R)$ a faithfully flat $R$-module?
145161
Testing whether an element of a tensor product of modules is zero
77297
Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$
57981
Alternative proof of $a\times0= 0$
105141
$\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
121663
If $a$ is a zero divisor of $\mathbb{F}$, then does $a$ fail to have a multiplicative inverse?
15184
$C \otimes A \cong C \otimes B$ does not imply $A \cong B$
1117
Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
114254
Zero divisors in $A[x_1,x_2,\dots,x_r]$
130297
$A$ be a subset of $[0,1]$ with non-empty interior ; then is it true that $\mathbb Q+A=\mathbb R$?
35353
Isomorphic quotient groups $\frac{G}{H} \cong \frac{G}{K}$ imply $H \cong K$?
91962
In a ring $a*a=0$ then $a+a=0$