If $A/I \cong A/J$ as rings and $I\subseteq J,$ then $I=J.$
70320
Let $R$ be a commutative Noetherian ring (with unity), and let $I$ be an ideal of $R$ such that $R/I \cong R$. Then is $I=(0)$?
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
63171
Translate of an ideal by $a$ coincides with the ideal iff  $a \in I$
73689
A question about the equivalence relation on the localization of a ring.
103518
If $J$ is the ideal generated by all idempotents in a prime ideal, then $R/J$ has only trivial idempotents
85129
If $H_1, H_2\leq G$ are such that $H_1\cong H_2$ then $G/H_1\cong G/H_2$?
14873
$1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent
35800
If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
66313
$\mathbb{Z}[i]/(a+bi) \cong \mathbb{Z}_{a^2+b^2}$ if $(a,b)=1$
49768
If Gal(K,Q) is abelian then |Gal(K,Q)|=n
75520
If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative.
41080
If A, B, and C are set and $A \subset B ,B \subset C \rightarrow A \subset C$
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
156910
Necessary and sufficient condition for $R/IJ \cong R/I \times R/J$
72507
Does $ab=1$ imply $ba=1$ in a ring?
92962
Rings with $a^5=a$ are commutative