Does $M_n(R_1)\cong M_n(R_2)$ imply $R_1\cong R_2$?
3778
If the matrix rings over two Rings of the same size are isomorphic, then the scalar rings are isomorphic
148569
Embeddings $A → B → A$, but $A \not\cong B$?
77297
Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$
14259
If M+N and M$\cap$N are finitely generated modules, so are M and N.
139595
Show that $(l_1)^* \cong l_{\infty}$
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
47385
Is $F = G\dfrac{{m_1}{m_2}}{r^2}$ really true?
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
75614
Proving that $n|m\implies f_n|f_m$
4648
Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$
77969
Question about proof for $S_4 \cong V_4 \rtimes S_3$
105951
Does $G\times K\cong H\times K$ imply $G\cong H$?
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
70861
$\mathbb P^n\times \mathbb P^m\not\cong \mathbb P^{m+n}$
27056
$ gl(2,\mathbb C) \cong sl(2,\mathbb C) \oplus \mathbb C $
74974
When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module?