Talk:Idempotent Elements of Ring with No Proper Zero Divisors

Could generalize second part to any idempotent of cancellative semigroup is the identity.

Also concept of "group with zero" as an inverse semigroup that has unique idempotent zero and unique idempotent group zero implies this result and comes from general treatment of inverse semigroups that provides useful generalization of groups (ie defines unique inverses and shows inverse is an involutory anti-automorphism that leaves idempotents fixed).