# irreducible

## Contents

## EnglishEdit

### EtymologyEdit

### PronunciationEdit

- IPA
^{(key)}: /ˌɪɹɪˈdjuːsɪbəl/

### AdjectiveEdit

**irreducible** (*comparative* **more irreducible**, *superlative* **most irreducible**)

- 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.

#### AntonymsEdit

- reducible
- (unable to be reduced): unincreasable

#### Derived termsEdit

### NounEdit

**irreducible** (*plural* **irreducibles**)

- (mathematics) Such a polynomial