Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
An exact sequence is a concept in mathematics, especially in group theory, ring and module theory, homological algebra, as well as in differential geometry.
In Lie theory and representation theory, the Levi decomposition, conjectured by Killing and Cartan and proved by, states that any finite-dimensional real Lie algebra g is the semidirect product of a solvable ideal and a semisimple subalgebra.
In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.
In mathematics, more specifically ring theory, an ideal, I, of a ring is said to be a nilpotent ideal, if there exists a natural number k such that Ik.
In algebra, the nilradical of a commutative ring is the ideal consisting of the nilpotent elements of the ring.
In the mathematical field of Lie theory, the radical of a Lie algebra \mathfrak is the largest solvable ideal of \mathfrak.
In mathematics, a Lie algebra is reductive if its adjoint representation is completely reducible, whence the name.