Definition of "irreducible"

irreducible

/ˌɪɹɪˈdjuːsɪbəl/

adjective
comparative more irreducible, superlative most irreducible
1. Not able to be reduced or lessened.
  Quotations
  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.
  1948 January and February, Cecil J. Allen, “British Locomotive Practice and Performance”, in Railway Magazine, page 48
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) that its only divisors are units and associates.
7. (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
8. (group theory, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.
noun
plural irreducibles
1. (mathematics) Such a polynomial