Idempotent (ring theory)

In ring theory, an element \( a \) of a ring \( R \) is said to be **idempotent** if it satisfies the condition: \[ a^2 = a. \] In other words, when you multiply the element by itself, you get the same element back. Idempotent elements play a significant role in various areas of algebra, particularly in the study of ring structure and module theory.