Units and Nilpotents
17895
Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
20613
Units (invertibles) of polynomial rings over a field
14403
If $n = p_1^{a_1} ... p_r^{a_r}$ the set of nilpotents of $\mathbb{Z}_n$ is $(p_1 p_2 ... p_{r-1} p_r)\Bbb Z_n$
121100
Rootspaces are $\mathop{ad}$ nilpotent
96144
Every element outside the maximal ideal of a local ring is a unit
103830
Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
137201
Classifying $\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z} / \langle(3,3,3)\rangle$
25009
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent
144531
How to prove that a nilpotent operator has a basis representation that is strictly upper triangular?
145364
units in indefinite integral
118911
Classifying Unital Commutative Rings of Order $p^2$
92822
Finite number of elements generating the unit ideal of a commutative ring
38346
Commutative Ring: Nilpotent elements closed under addition?
68915
What are the units in $\mathbb{Z}[\root 3 \of 2]$?
54358
Why $(1-\zeta)$ unit where $\zeta$ is a primitive nth and n divisible by two primes
52966
Rings, ideals and units-proof
77799
Determine the set of units $(\Bbb Z/n\Bbb Z)^\times$ for different values of $n$