irreducible

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irreducible

/ˌɪɹɪˈdjuːsɪbəl/

adjective

not comparable Not able to be reduced or lessened. With each reduction in the number of railways, there must come, eventually, a decline in interest, if only through reduction in variety; and when it comes to one nationalised railway only we have reached the irreducible minimum.
Opposite: unincreasable
not comparable Not able to be brought to a simpler or reduced form.
not comparable, of a polynomial Unable to be factorized into polynomials of lower degree, as (x² + 1).
not comparable, of a fraction Whose numerator and denominator share no common factor greater than 1.
not comparable, of an integer Unable to be factored into smaller integers; prime.
not comparable, of an element of a ring Whose only divisors are units and associates.
not comparable, of an algebraic variety Inexpressible as the union of two proper algebraic subvarieties.
not comparable, of a manifold Not containing a sphere of codimension 1 that is not the boundary of a ball.
not comparable, of a representation Impossible to divide further into representations of lower dimension by means of any similarity transformation.

Opposite: reducible

noun irreducibles

Such a polynomial

Thesaurus

adjective

Opposite: reducible

Translations

Every language

adj not able to be reduced or lessened

Español	irreductible
日本語	減らせない herasenai
Português	irredutível
Français	irréductible
Italiano	irriducibile

adj (mathematics, of an integer) unable to be factored into smaller integers

Español	irreducible
日本語	既約の kiyaku no
Français	irréductible
Русский	неприводимый neprivodimyj

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MLA

"irreducible." Wiktionary, via Micwyn, micwyn.com/word/irreducible. Accessed 6 Nov. 2026.

APA

irreducible. (n.d.). In Wiktionary, via Micwyn. Retrieved November 6, 2026, from https://micwyn.com/word/irreducible

Chicago

"irreducible." Wiktionary, via Micwyn. Accessed November 6, 2026. https://micwyn.com/word/irreducible.

BibTeX

@misc{irreducible_2026,
  title = {irreducible},
  howpublished = {Wiktionary, via Micwyn},
  year = {2026},
  url = {https://micwyn.com/word/irreducible},
  urldate = {2026-11-06}
}