irreducible

Such a polynomial

Not able to be reduced or lessened.

Not able to be brought to a simpler or reduced form.

Unable to be factorized into polynomials of lower degree, as (x² + 1).

Whose numerator and denominator share no common factor greater than 1.

Unable to be factored into smaller integers; prime.

Whose only divisors are units and associates.

Inexpressible as the union of two proper algebraic subvarieties.

Not containing a sphere of codimension 1 that is not the boundary of a ball.

Impossible to divide further into representations of lower dimension by means of any similarity transformation.