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What does irreducible mean?

Looking for the meaning or definition of the word irreducible? Here's what it means.

Adjective
  1. Not able to be reduced or lessened.
  2. Not able to be brought to a simpler or reduced form.
  3. (mathematics) Unable to be factorized into polynomials of lower degree, as (x^2 + 1).
  4. (mathematics) Unable to be factored into smaller integers; prime.
  5. (manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
  6. (representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.
Noun
  1. (mathematics) Such a polynomial
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