irreducible

adj

1. (not-comparable)Not 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.”

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

noun

1. Such a polynomial