If $M \otimes N \cong M' \otimes N$, is it true that $M \cong M'$?
15184
$C \otimes A \cong C \otimes B$ does not imply $A \cong B$
122581
Prove or disprove that $G_1/H_1 \cong G_2/H_2$
118898
Is there a simple way of proving that $\text{GL}_n(R) \not\cong \text{GL}_m(R)$?
156909
$\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups.
16172
My proof of $I \otimes N \cong IN$ is clearly wrong, but where have I gone wrong?
5223
$\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
148569
Embeddings $A → B → A$, but $A \not\cong B$?
132587
Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
156910
Necessary and sufficient condition for $R/IJ \cong R/I \times R/J$
43987
Decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields
52530
There exists a prime congruent to $m$ mod $p$
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
17191
How to verify $H\otimes K \cong \bigoplus\limits_{i\in I}H$
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
51898
Show that $\operatorname{Hom}_{R} (R,M) \cong M$