Ring/Nilpotent Proof
14873
$1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent
50404
How to prove a matrix is nilpotent?
151803
Prove that $R$ is commutative
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
126331
Associative ring with identity, inverses, divisors of zero and Artinianity
6646
A (non-artificial) example of a ring without maximal ideals
103830
Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
112701
Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
107900
A ring which has many distinct left inverses
69649
If an ideal contains the multiplicative identity, then it is the whole ring
50908
Showing a Ring and an Ideal are equal
45523
Can the product of two non invertible elements in a ring be invertible?
61526
An exercise about nilpotent quotient groups
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
154613
Showing a set of fractions is a ring
22563
Units and Nilpotents
39576
Quotient ring being isomorphic to the initial ring