idempotent
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English[edit]
Etymology[edit]
Latin roots, idem (“same”) + potent (“having power”) – literally, “having the same power”.
Coined 1870 by American mathematician Benjamin Peirce in context of algebra.^{[1]}
Pronunciation[edit]
Adjective[edit]
idempotent (not comparable)
 (mathematics, computing) 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.
 A projection operator is idempotent.
 (mathematics) 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.
 Every finite semigroup has an idempotent element.
 Every group has a unique idempotent element: namely, its identity element.
 (mathematics) Said of a binary operation: that all of the distinct elements it can operate on are idempotent (in the sense given just above).
 Since the AND logical operator is commutative, associative, and idempotent, then it distributes with respect to itself.
 (mathematics) Said of an algebraic structure: having an idempotent operation (in the sense above).
Usage notes[edit]
See the Usage notes section of nullipotent.
Coordinate terms[edit]
Related terms[edit]
Translations[edit]
mathematics: an action which, when performed multiple time, has no further effect on its subject after the first time it is performed


mathematics: Said of an element of an algebraic structure with a binary operation: that when the element operates on itself, the result is equal to itself


Said of a binary operation: that all of the distinct elements it can operate on are idempotent
Noun[edit]
idempotent (plural idempotents)
 (mathematics) An idempotent element.
 (mathematics) An idempotent structure.
References[edit]
 ^ Polcino & Sehgal (2002), p. 127
 “idempotent” at FOLDOC
German[edit]
Pronunciation[edit]
Audio (file)
Adjective[edit]
idempotent
Swedish[edit]
Adjective[edit]
idempotent
Turkish[edit]
Adjective[edit]
idempotent
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