## irreducible

[ir′i do̵̅o̅s**′**ə bəl, -dyo̵̅o̅s

**′**-]

adjective

that cannot be reduced

*Related Forms:*

- irreducibility
noun

- irreducibly
adverb

## irreducible

adjective

Impossible to reduce to a desired, simpler, or smaller form or amount:

*irreducible burdens.**Related Forms:*

**ir′re·duc′i·bil′i·ty**,**ir′re·duc′i·ble·ness**noun

**ir′re·duc′i·bly**adverb

## irreducible

Adjective

(*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

Antonyms

- reducible
- (unable to be reduced): unincreasable

Noun

(*plural* irreducibles)

- (mathematics) Such a polynomial

Origin

*ir-* + *reducible*