# Definition of Irreducible. Meaning of Irreducible. Synonyms of Irreducible

Here you will find one or more explanations in English for the word Irreducible. Also in the bottom left of the page several parts of wikipedia pages related to the word Irreducible and, of course, Irreducible synonyms and on the right images related to the word Irreducible.

## Definition of Irreducible

Irreducible
Irreducible Irre*du"ci*ble, a. 1. Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition; as, an irreducible hernia. 2. (Math.) Incapable of being reduced to a simpler form of expression; as, an irreducible formula. Irreducible case (Alg.), a particular case in the solution of a cubic equation, in which the formula commonly employed contains an imaginary quantity, and therefore fails in its application. -- Irre*du"ci*ble*ness, n. -- -- Ir`re*du"ci*bly, adv.

## Meaning of Irreducible from wikipedia

- Irreducible complexity (IC) involves the idea that certain biological systems cannot evolve by successive small modifications to pre-existing functional...
- In mathematics, an irreducible polynomial (or prime polynomial) is, roughly speaking, a non-constant polynomial that cannot be factored into the product...
- specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic...
- element in an integral domain is said to be irreducible if it is not a product of two non-units. Irreducible elements should not be confused with prime...
- An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers...
- In mathematics, the concept of irreducibility is used in several ways. A polynomial over a field may be an irreducible polynomial if it cannot be factored...
- The principle of Irreducibility, in philosophy, has the sense that a complete account of an entity will not be possible at lower levels of explanation...
- In mathematics, specifically in algebraic geometry, the concept of irreducible component is used to formalize the idea that an algebraic set such as the...
- especially in the field of ring theory, the term irreducible ring is used in a few different ways. A (meet-)irreducible ring is one in which the intersection of...
- absolutely irreducible if it is irreducible over the complex field. For example, x 2 + y 2 − 1 {\displaystyle x^{2}+y^{2}-1} is absolutely irreducible, but...