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.

   Antonym: 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. (number theory, of a fraction) Whose numerator and denominator share no common factor greater than 1.
5. (number theory, of an integer) Unable to be factored into smaller integers; prime.
6. (algebra, of an element of a ring) that its only divisors are units and associates.
7. (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
8. (group theory, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.

Antonyms

• reducible

Derived terms

• irreducibility
• irreducible complexity
• irreducibleness
• irreducibly
• irrep

 

Translations

not able to be reduced or lessened

• Bulgarian: неподлежащ на намаление (nepodležašt na namalenie)
• Catalan: irreductible
• (deprecated template usage) {{trans-mid}}
• Irish: dochloíte, dosháraithe
• Japanese: 減らせない (herasenai)

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

• Bulgarian: несъкратим (nesǎkratim)
• (deprecated template usage) {{trans-mid}}
• Japanese: 既約の (kiyaku no)

Noun

irreducible (plural irreducibles)

1. (mathematics) Such a polynomial

---

Spanish

Adjective

irreducible m or f (masculine and feminine plural irreducibles)

1. irreducible

Further reading

• “irreducible”, in Diccionario de la lengua española, Vigésima tercera edición, Real Academia Española, 2014