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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.

A unar is an algebra A=(A,f), where f is a single unary operation.

A set considered together with the sigma-algebra on the set.