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A Lie algebra over an algebraically closed field is called exceptional if it is constructed from one of the root systems E_6, E_7, E_8, F_4, and G_2 by the Chevalley ...

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

Every polynomial equation having complex coefficients and degree >=1 has at least one complex root. This theorem was first proven by Gauss. It is equivalent to the statement ...

Denoted sl_n.

An algebra S^' which is part of a large algebra S and shares its properties.

A finite division algebra is a field.

A finite-dimensional Lie algebra all of whose elements are ad-nilpotent is itself a nilpotent Lie algebra.

A generalization of a Heyting algebra which replaces Boolean algebra in "intuitionistic" logic.

An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.