The sum of a vertible element and a nilpotent element is vertible
22563
Units and Nilpotents
108742
Proving commutativity of addition for vector spaces
10908
Associated elements in a ring
3392
Sum of products of elements of nonempty subsets of A set
1125
Inductive proof that ${2n\choose n}=\sum{n\choose i}^2.$
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$
158426
Proving lemma about centrality of idempotent elements in a Ring with no nilpotent elements.
144082
Every $n\times n$ matrix is the sum of a diagonalizable matrix and a nilpotent matrix.
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
66968
if $a,b$ are nilpotent elements of a commutative ring $R$, show that $a+b$ is also nilpotent
16593
Irreducible Spectrum implies Zero-Divisors are Nilpotent
1577
Order of nontrivial elements is 2 implies Abelian group
119671
Is there an infinite dimensional $V$ such that every linear operator on $V$ is a direct sum of a nilpotent and  an invertible operator?
56097
If $A$ and $AB-BA$ commute, show that $AB-BA$ is nilpotent
20309
Product and sum of positive operators is positive
50266
In the following figure prove that: $AK||BC$
134844
Summablity and countability