Prove $1+x$ is a unit in $R: \text{commutative ring}$ where $x$ is nilpotent
22563
Units and Nilpotents
88307
Commutative property of ring addition
130004
Jacobson radical equal to nilradical in $R[X]$
59286
Given X is Uni, Prove -X is Uni?
13162
Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit
119067
Basic Ring Theory Question involving the unit element
16023
Are associates unit multiples in a commutative ring with $1$?
99715
Proper ideal and units proof
55018
Prove that $A^*A + I$ is invertible
148550
Units in quotient ring of $\mathbb Z[X]$
92420
Characteristic of  a Non-unital Integral Ring
81296
If A and B are ideals of a ring, show that A + B = $\{a+b|a \in A, b \in B\}$ is an ideal
103830
Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
91962
In a ring $a*a=0$ then $a+a=0$
50241
Cardinality of the quotient ring $\mathbb Z_5[i]/\langle 1+i\rangle$
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
7034
Prove that $A+I$ is invertible if $A$ is nilpotent