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The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwārizmī about algebraic methods. In modern usage, algebra has several meanings. One use of the ...

A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not ...

An involutive Banach algebra is a Banach algebra A which is an involutive algebra and ||a^*||=||a|| for all a in A.

Let K be a class of topological spaces that is closed under homeomorphism, and let X be a topological space. If X in K and for every Y in K such that X subset= Y, X is a ...

Linear Algebra

Let A and B be two algebras over the same signature Sigma, with carriers A and B, respectively (cf. universal algebra). B is a subalgebra of A if B subset= A and every ...

The roots of a semisimple Lie algebra g are the Lie algebra weights occurring in its adjoint representation. The set of roots form the root system, and are completely ...

A function which is not an algebraic function. In other words, a function which "transcends," i.e., cannot be expressed in terms of, algebra. Examples of transcendental ...

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

Differential algebra is a field of mathematics that attempts to use methods from abstract algebra to study solutions of systems of polynomial nonlinear ordinary and partial ...