$1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent
22563
Units and Nilpotents
32772
Proving units in a ring
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
78298
On the nilpotence of the matrix $AB-BA$
156443
if $x$ and $y$ commute with $[x y]$, then $[x y]$ is nilpotent
133758
Traces of powers of a matrix $A$ over an algebra are zero implies $A$ nilpotent.
31917
If $q$ is coprime to $a$ then $a\mid nq-1,\,$ so $q$ is invertible mod $a$
20877
The set of all nilpotent elements is an ideal
158695
Prove that if $AB$ is invertible then $B$ is invertible.
57123
Jacobson radical of a finitely generated $\mathbb Z$-algebra is nilpotent
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
126331
Associative ring with identity, inverses, divisors of zero and Artinianity
20613
Units (invertibles) of polynomial rings over a field
130268
How to prove that a nilpotent matrix is not invertible?
117482
Lifting idempotents modulo a nilpotent ideal
57543
Show that a matrix is nilpotent.
18971
Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$