irreducible

1. not comparableNot able to be reduced or lessened.

   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

   Antonyms: unincreasable

2. not comparableNot able to be brought to a simpler or reduced form.
3. not comparablemathematicsUnable to be factorized into polynomials of lower degree, as (x² + 1).
4. not comparablemathematicsWhose numerator and denominator share no common factor greater than 1.
5. not comparablemathematicsUnable to be factored into smaller integers; prime.
6. not comparablealgebraWhose only divisors are units and associates.
7. not comparablealgebraic geometryInexpressible as the union of two proper algebraic subvarieties.
8. not comparablemathematicsNot containing a sphere of codimension 1 that is not the boundary of a ball.
9. not comparablegroup theoryImpossible to divide further into representations of lower dimension by means of any similarity transformation.

plural irreducibles

1. mathematicsSuch a polynomial