irreducible

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Pronunciation

• IPA: /ˌɪɹɪˈdjuːsɪbəl/

Adjective

irreducible

1. Not able to be reduced or lessened.

   Antonyms: unincreasable

2. Not able to be brought to a simpler or reduced form.
3. (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x² + 1).
4. (mathematics, of an integer) Unable to be factored into smaller integers; prime.
5. (algebra, of an element of a ring) that its only divisors are units and associates.
6. (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
7. (group theory, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.

Antonyms

• reducible

Noun

irreducible (plural irreducibles)

1. (mathematics) Such a polynomial

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