One of my homework problems asks us to prove that let $S$ be a subset of a ring $A$, the localization $A[S^{-1}]$ is an idempotent $A$-algebra. I don't remember my instructor defining an "idempotent $A$-algebra" in class. The assignment is due soon so I probably won't have time to ask him. Could anyone help clarify what is an idempotent $A$-algebra?
Thank you!