Failure of Idempotent Lifting
- Pure Mathematics -
Algebra Dictionary
Definition
A situation in a ring or algebra surjection π: A → A/I where an idempotent e ∈ A/I (e^2 = e) does not admit any idempotent p ∈ A with π(p) = e; the quotient contains a projector that has no idempotent preimage in the source.