• Said of a function: describing an action which, when performed multiple times on the same subject, has no further effect on its subject after the first time it is performed.
  • Said of an element of an algebraic structure with a binary operation (such as a group or semigroup): when the element operates on itself, the result is equal to itself.
  • Said of a binary operation: such that all of the distinct elements it can operate on are idempotent (in the sense given just above).
  • Said of an algebraic structure: having an idempotent operation (in the sense above).


  • An idempotent element.
  • An idempotent structure.


  • Latin roots, idem + potent – literally, “having the same power”.
  • Coined 1870 by American mathematician Benjamin Peirce in context of algebra.

Modern English dictionary

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