Can a nilpotent element be an idempotent?
42528
Prove that every idempotent element is not nilpotent element.
16593
Irreducible Spectrum implies Zero-Divisors are Nilpotent
103500
Nilpotent Jacobson radical
18361
Does the unit generate the additive group in a unital ring with cyclic additive group?
15904
Prime ideal and nilpotent elements
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?
122845
Does an inseparable extension have a purely inseparable element?
2884
$m,n>1$ are relatively prime integers , then are there at-least four idempotent (w.r.t. multiplication) elements in $\mathbb Z_{mn}$ ?
52354
Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
45523
Can the product of two non invertible elements in a ring be invertible?
130268
How to prove that a nilpotent matrix is not invertible?
117546
Idempotent of closure and other properties
129610
Why is the direct product of a finite number of nilpotent groups nilpotent?
50404
How to prove a matrix is nilpotent?
72350
Constructing Idempotent Generator of Idempotent Ideal
119684
Is a contraction idempotent operator self-adjoint?
109649
idempotents acting as local identities