irreducible

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English

Etymology

ir- +‎ reducible

Pronunciation

  • IPA(key): /ˌɪɹɪˈdjuːsɪbəl/

Adjective

irreducible (comparative more irreducible, superlative most irreducible)

  1. Not able to be reduced or lessened.
    Antonym: unincreasable
    • 1948 January and February, Cecil J. Allen, “British Locomotive Practice and Performance”, in Railway Magazine, page 48:
      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.
  2. Not able to be brought to a simpler or reduced form.
  3. (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x2 + 1).
  4. (number theory, of a fraction) Whose numerator and denominator share no common factor greater than 1.
  5. (number theory, of an integer) Unable to be factored into smaller integers; prime.
  6. (algebra, of an element of a ring) Whose only divisors are units and associates.
  7. (algebraic geometry, of an algebraic variety) Inexpressible as the union of two proper algebraic subvarieties.
  8. (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
  9. (group theory, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.

Antonyms

Derived terms

Translations

Noun

irreducible (plural irreducibles)

  1. (mathematics) Such a polynomial

Spanish

Pronunciation

  • IPA(key): (Spain) /ireduˈθible/
  • IPA(key): (Latin America) /ireduˈsible/
  • Rhymes: -ible
  • Syllabification: i‧rre‧du‧ci‧ble

Adjective

irreducible m or f (masculine and feminine plural irreducibles)

  1. irreducible

Further reading

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