- Not able to be reduced or lessened.
- Not able to be brought to a simpler or reduced form.
- (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x^2 + 1).
- (mathematics, of an integer) Unable to be factored into smaller integers; prime.
- (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
- (group theory, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.
irreducible (plural irreducibles)
- (mathematics) Such a polynomial