idempotent

Etymology
roots, – literally, “having the same power”.

Coined in 1870 by American mathematician in the context of algebra.

Adjective

 * 1)   Such that, when performed multiple times on the same subject, it has no further effect on its subject after the first time it is performed.
 * A projection operator is idempotent.
 * 1)   Such that, when it operates on itself, the result is equal to itself.
 * Every finite semigroup has an idempotent element.
 * Every group has a unique idempotent element: namely, its identity element.
 * 1)   Such that all of the distinct elements it can operate on are idempotent.
 * Since the AND logical operator is commutative, associative, and idempotent, it distributes with respect to itself.
 * 1)   Having an idempotent operation.

Usage notes
See the Usage notes section of .

Translations

 * Chinese:
 * Mandarin:
 * Czech:
 * Danish: idempotent
 * Esperanto: idempotento
 * Finnish:
 * German:
 * Icelandic: sjálfvalda
 * Japanese: 冪等
 * Polish: idempotentny
 * Russian:
 * Swedish:
 * Turkish: idempotent


 * Chinese:
 * Mandarin:
 * Esperanto: idempotento
 * Finnish:
 * Greek: ταυτοδύναμος
 * Spanish:


 * Finnish:

Noun

 * 1)  An idempotent element.
 * 2)  An idempotent structure.

Adjective

 * 1) idempotent

Adjective

 * 1) idempotent