Irreducible

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.

Adj.

1.

irreducible - incapable of being made smaller or simpler; "an irreducible minimum"; "an irreducible formula"; "an irreducible hernia" Antonyms: reducible - capable of being reduced; "reducible to a set of principles of human nature"- Edmund Wilson

a certain, an, any, any one, atomic, austere, bare, basic, called for, chaste, deep-seated, either, elementary, esoteric, essential, exclusive, fundamental, homely, homespun, homogeneous, immanent, implanted, implicit, inalienable, indicated, indispensable, individual, indivisible, indwelling, inextricable, infixed, ingrained, inherent, inner, integral, internal, intrinsic, inward, inwrought, irreductible, irreplaceable, lone, mere, monadic, monistic, monolithic, necessary, needed, needful, of a piece, one, plain, prerequisite, primal, primary, private, pure, pure and simple, required, requisite, resident, secret, severe, simon-pure, simple, single, singular, sole, solid, solitary, spare, stark, subjective, unadorned, unalienable, unanalyzable, unchallengeable, uncluttered, undifferenced, undifferentiated, undivided, unforgoable, uniform, unique, unitary, unquestionable, unsolvable, vital, wanted, whole