AAR13
From Exampleproblems
Let 
be a nilpotent element of the commutative ring 
. Let 
for minimal 
. Deduce that the sum of nilpotent element and a unit is a unit.
If the nilpotent element is 0 then the sum is the unit. If the nilpotent element is a zero divisor for some nonzero element of the ring, multipying the sum by the nonzero element and then by its inverse will give a unit.
