irreducible
Pronunciation
  • IPA: /ˌɪɹɪˈdjuːsɪbəl/
Adjective

irreducible

  1. Not able to be reduced or lessened.
    Antonyms: unincreasable
  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. (mathematics, of an integer) Unable to be factored into smaller integers; prime.
  5. (algebra, of an element of a ring) that its only divisors are units and associates.
  6. (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
  7. (group theory, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.
Antonyms Noun

irreducible (plural irreducibles)

  1. (mathematics) Such a polynomial



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