Show $\Bbb{Z}_m\otimes_{\Bbb{Z}}\Bbb{Z}_n=0$ if and only if $m,n$ are coprime.
63803
Calculating the tensor product $\mathbb{Z}/n\mathbb{Z} \otimes_{\mathbb Z} \mathbb{Z}/n\mathbb{Z}$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
33560
Show that matrices $A$ and $B$ commute if and only if $\begin{vmatrix} b & a-c \\ e & d-f\end{vmatrix}=0.$
141258
Why does $M \mathbin{\otimes_R} N \cong M_\mathfrak{p} \mathbin{\otimes_{R_\mathfrak{p}}} N$?
80601
Let $a,b$ be in a group $G$. Show $(ab)^n=a^nb^n$ $\forall n\in\mathbb{Z}$ if and only if $ab=ba$.
59533
If $\gcd(m,n)=1$, then $\mathbb{Z}_n \times \mathbb{Z}_m$ is cyclic.
54430
For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
118452
how to prove $\mathbb Z_n$ has divisors of zero if and only if $n$ is not prime
137029
Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.
9794
Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime
122932
When $(\mathbb{Q}(\zeta_n) : \mathbb{Q}) = 2$?
30404
Is $\mathbb{Z}/3\otimes \mathbb{Z}[1/2]=\mathbb{Z}/3$?
98284
show $\Bbb Z_6 \cong \Bbb Z_3 \times \Bbb Z_2 $.
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
146980
Zero divisors of $\mathbb{Z}×\mathbb{Z}×\mathbb{Z}$
83713
If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$