Irreducible (definition) by Webster 1913

Ir`re*du"ci*ble (?), a.

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.

-- Ir`re*du"ci*ble*ness, n. -- -- Ir`re*du"ci*bly, adv.

Eisenstein's irreducibility criterion	prime	representations of Lie algebras	unique factorization domain
principal ideal domain	Fundamental theorem of algebra	All finite fields are isomorphic to GF(p^n)	Polynomial
Markov chain	simple	unit	Kronecker's Theorem
Proof of the uniqueness of splitting fields	irreducibility of cyclotomic polynomials	unique factorization of polynomials	Gauss's Lemma
rational functions in one variable	Gaussian integer	minimal polynomial	cyclotomic polynomial
ring theory	Separable	monism