The Stacks project

Exercise 111.1.10. Let $A$ be a ring and let $I \subset A$ be a locally nilpotent ideal. Show that the map $A \to A/I$ induces a bijection on idempotents. (Hint: It may be easier to prove this when $I$ is nilpotent. Do this first. Then use “absolute Noetherian reduction” to reduce to the nilpotent case.)