• (adj): Incapable of being made smaller or simpler.
    Example: "An irreducible minimum"; "an irreducible formula"; "an irreducible hernia"

Some articles on irreducible:

Subdirectly Irreducible Algebra
... universal algebra (and in its applications), a subdirectly irreducible algebra is an algebra that cannot be factored as a subdirect product of "simpler" algebras ... Subdirectly irreducible algebras play a somewhat analogous role in algebra to primes in number theory ...
Train Track Map - Main Result For Irreducible Automorphisms - Bestvina–Handel Theorem For Irreducible Automorphisms - Applications To Growth
... requiring additional arguments) of the above theorem is the following If φ ∈ Out(Fk) is irreducible then the Perron–Frobenius eigenvalue λ(f) does not depend on the choice of a train track ... If φ ∈ Out(Fk) is irreducible and of infinite order then λ(φ) > 1 ... Unlike for elements of mapping class groups, for an irreducible φ ∈ Out(Fk) it is often the case that λ(φ) ≠ λ(φ−1) ...
Absolutely Irreducible
... In mathematics, absolutely irreducible is a term applied to linear representations or algebraic varieties over a field ... It means that the object in question remains irreducible, even after any finite extension of the field of coefficients ... In both cases, being absolutely irreducible is the same as being irreducible over the algebraic closure of the ground field ...
Langlands Classification - Classification
... The Langlands classification states that the irreducible admissible representations of (g,K) are parameterized by triples (F, σ,λ) where F is a subset of Δ Q is ... More precisely, the irreducible admissible representation given by the data above is the irreducible quotient of a parabolically induced representation ...
Special Linear Lie Algebra - Representation Theory Of
... Let be a finite irreducible representation of, and let be an eigenvector of with the highest eigenvalue ... Therefore, for each, there is a unique, up to isomorphism, irreducible representation of dimension spanned by elements.. ... The beautiful special case of shows a general way to find irreducible representations of Lie Algebras ...

Famous quotes containing the word irreducible:

    If an irreducible distinction between theatre and cinema does exist, it may be this: Theatre is confined to a logical or continuous use of space. Cinema ... has access to an alogical or discontinuous use of space.
    Susan Sontag (b. 1933)