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Algebra is a branch of mathematics. The term is used in combinations such as homological algebra, commutative algebra, linear algebra, multilinear algebra, and topological algebra.

An algebraic system, consisting of a set with a family of algebraic operations.

A special case of an operator ring: An algebra (occasionally, a linear or vector algebra) over a field, over a skew-field or over a commutative ring. Associative algebras (formerly described as "hypercomplex systems" ) and non-associative algebras are algebras in this sense.

A synonym of universal algebra. This includes algebras such as Boolean algebras, unary algebras, etc.

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