irreducible

English

Etymology

ir- +‎ reducible

Pronunciation

• IPA^(key): /ˌɪɹɪˈdjuːsɪbəl/

Adjective

irreducible (comparative more irreducible, superlative most irreducible)

1. Not able to be reduced or lessened.
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.

Translations

not able to be reduced or lessened

• Bulgarian: неподлежащ на намаление (nepodležašt na namalenie)
• (deprecated template usage) {{trans-mid}}

(mathematics, of an integer) unable to be factored into smaller integers

• Bulgarian: несъкратим (nesǎkratim)
• (deprecated template usage) {{trans-mid}}

Antonyms

• reducible
• (unable to be reduced): unincreasable

Derived terms

• irreducibility
• irreducible complexity
• irreducibleness
• irreducibly
• irrep

 

Noun

irreducible (plural irreducibles)

1. (mathematics) Such a polynomial