idempotent

English

Etymology

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

Pronunciation

• (US) IPA^(key): /aɪ.dəmˈpoʊ.tənt/, /ɪ.dəmˈpoʊ.tənt/, /aɪˈdɛm.pə.tənt/

• Audio (US):

  (file)

Adjective

idempotent (not comparable)

1. (mathematics, computing) (said of a function) 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.

2. (mathematics) (said of an element of an algebraic structure with a binary operation, such as a group or semigroup) 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.

3. (mathematics) (said of a binary operation) Such 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, it distributes with respect to itself.

4. (mathematics) (said of an algebraic structure) Having an idempotent operation (in the sense given above).

Usage notes

• See the Usage notes section of nullipotent.

Coordinate terms

• nilpotent
• nullipotent

Related terms

• idempotence
• nilpotent
• nullipotent
• unipotent

Translations

mathematics: an action which, when performed multiple time, has no further effect on its subject after the first time it is performed

• Chinese:

  Mandarin: 冪等／幂等 (zh) (mìděng)

• Czech: idempotentní (cs)
• Danish: idempotent
• Esperanto: idempotento
• Finnish: idempotentti (fi)
• German: idempotent (de)
• Icelandic: sjálfvalda
• Japanese: 冪等 (べきとう, bekitō)
• Polish: idempotentny
• Russian: идемпоте́нтный (ru) (idempoténtnyj)
• Swedish: idempotent (sv)
• Turkish: idempotent

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

• Chinese:

  Mandarin: 冪等／幂等 (zh) (mìděng)

• Esperanto: idempotento
• Finnish: idempotentti (fi)
• Greek: ταυτοδύναμος m (taftodýnamos)
• Spanish: idempotente (es)

Said of a binary operation: that all of the distinct elements it can operate on are idempotent

• Finnish: idempotentti (fi)

See also

• involutory

Noun

idempotent (plural idempotents)

1. (mathematics) An idempotent element.
2. (mathematics) An idempotent structure.

References

• “idempotent” at FOLDOC

French

Pronunciation

• Audio:

  (file)

Adjective

idempotent (feminine idempotente, masculine plural idempotents, feminine plural idempotentes)

1. idempotent

German

Pronunciation

• Audio:

  (file)

Adjective

idempotent (strong nominative masculine singular idempotenter, not comparable)

1. idempotent

Declension

Positive forms of idempotent (uncomparable)

number & gender		singular			plural
		masculine	feminine	neuter
predicative		er ist idempotent	sie ist idempotent	es ist idempotent	sie sind idempotent
strong declension (without article)	nominative	idempotenter	idempotente	idempotentes	idempotente
	genitive	idempotenten	idempotenter	idempotenten	idempotenter
	dative	idempotentem	idempotenter	idempotentem	idempotenten
	accusative	idempotenten	idempotente	idempotentes	idempotente
weak declension (with definite article)	nominative	der idempotente	die idempotente	das idempotente	die idempotenten
	genitive	des idempotenten	der idempotenten	des idempotenten	der idempotenten
	dative	dem idempotenten	der idempotenten	dem idempotenten	den idempotenten
	accusative	den idempotenten	die idempotente	das idempotente	die idempotenten
mixed declension (with indefinite article)	nominative	ein idempotenter	eine idempotente	ein idempotentes	(keine) idempotenten
	genitive	eines idempotenten	einer idempotenten	eines idempotenten	(keiner) idempotenten
	dative	einem idempotenten	einer idempotenten	einem idempotenten	(keinen) idempotenten
	accusative	einen idempotenten	eine idempotente	ein idempotentes	(keine) idempotenten

Swedish

Adjective

idempotent

1. idempotent

Turkish

Adjective

idempotent

1. idempotent