Definition:Irreducible


 * Ring Theory:
 * Irreducible Element: An element of an integral domain $D$ is irreducible it has no non-trivial factorization in $D$.
 * Irreducible Polynomial: A polynomial is irreducible over a field it cannot be represented as the product of two or more non-constant polynomials over that field.


 * Topology:
 * Irreducible Space: A topological space is irreducible it cannot be represented as a decomposition of closed sets.
 * Irreducible Subset: a subset of a topological space which is irreducible


 * Representation Theory:
 * Irreducible Linear Representation: A linear representation $\rho: G \to \GL V$ is irreducible  it has no non-trivial subspace $W$ which is invariant for every linear operator in the set $\set {\map \rho g: g \in G}$.
 * Irreducible $G$-Module: A $G$-module is irreducible its corresponding linear representation is irreducible.
 * Irreducible Representation (Lie Algebra)
 * Irreducible Representation (Topological Group)


 * Order Theory:
 * Meet Irreducible
 * Completely Irreducible


 * Incidence Geometry:
 * Irreducible Axiomatic Projective Space


 * Definition:Irreducible Algebraic Variety
 * Definition:Irreducible Scheme

Also see

 * Definition:Reducible