Idempotent (ring theory)
= Idempotent (ring theory)
{wiki=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.