Idempotent elements on the quotient ring
117482
Lifting idempotents modulo a nilpotent ideal
54585
Order of some quotient ring of Gaussian integers
103518
If $J$ is the ideal generated by all idempotents in a prime ideal, then $R/J$ has only trivial idempotents
4790
Generators of a finitely generated free module over a commutative ring
67944
Nilpotent Elements and Intersection of Prime Ideals
46843
A ring without the Invariant Basis Number property
19883
Prime ideals of the matrix ring
61526
An exercise about nilpotent quotient groups
103830
Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
52966
Rings, ideals and units-proof
63568
Ring with finitely many zerodivisors
15904
Prime ideal and nilpotent elements
92420
Characteristic of  a Non-unital Integral Ring
79650
Division Rings and Division Algebras
42552
Localisation is isomorphic to a quotient of polynomial ring
38346
Commutative Ring: Nilpotent elements closed under addition?
39576
Quotient ring being isomorphic to the initial ring