Let R be a commutative ring with 1 not equal to zero. Prove that if "a" is a nilpotent element of R then 1-ab is a unit for all "b" in R.© BrainMass Inc. brainmass.com September 23, 2018, 10:09 am ad1c9bdddf - https://brainmass.com/math/ring-theory/commutative-rings-nilpotent-elements-152928
since a is nilpotent, there is a positive integer n such that a^n = 0
observe that, in particular if ...
Commutative rings and nilpotent elements are investigated.