For all $A, B \in \mathcal{M}_n(\mathbb{C})$, if $[A, [A, B]] = 0$, then $[A, B]$ is nilpotent
57543
Show that a matrix is nilpotent.
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
65162
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
119452
Nilpotent matrices with same minimal polynomial and nullity
124460
Show that if $f \in \mathbb{C} \left[x_1, \dots, x_n \right]$ vanishes at every point of $\mathbb{Z}^n$, then $f$ is the zero polynomial.
78031
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
156443
if $x$ and $y$ commute with $[x y]$, then $[x y]$ is nilpotent
74318
Find the nilpotents in $\mathbb{Z}_3[x]/(x^2-1)$
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
158426
Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.
115273
Nilpotent matrix and basis for $F^n$
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
16593
Irreducible Spectrum implies Zero-Divisors are Nilpotent
83337
If $A ∈M_n(C)$ is such that $(Ax,x) = 0$ for all $x ∈C^n$, then $A = 0$