Algebra may refer to:
Branches of mathematics Elementary algebra Universal algebra Abstract algebra Linear algebra Relational algebra Computer algebra Homological algebra
Mathematical structures Vector space with multiplication Algebra over a field, or algebra, a vector space equipped with a bilinear vector product. In ring theory and linear algebra: Algebra over a commutative ring, a module equipped with a bilinear product. Generalization of algebras over a field Associative algebra, a module equipped with an associative bilinear vector product Superalgebra, a -graded algebra Lie algebras, Poisson algebras, and Jordan algebras, important examples of (potentially) nonassociative algebras In functional analysis: Banach algebra, an associative algebra A over the real or complex numbers which at the same time is also a Banach space Operator algebra, continuous linear operators on a topological vector space with multiplication given by the composition *-algebra, An algebra with a notion of adjoints C*-algebra, a Banach algebra equipped with a unary involution operation Von Neumann algebra (or W*-algebra) Coalgebra is the dual notion
Other structures A different class of "algebras" consists of objects which generalize logical connectives, sets, and lattices. In logic: Relational algebra, in which a set of finitary relations that is closed under certain operators Boolean algebra and Boolean algebra (structure) Heyting algebra In measure theory: Algebra over a set, a collection of sets closed under finite unions and complementation Sigma algebra, a collection of sets closed under countable unions and complementation
"Algebra" can also describe more general structures: In category theory and computer science: F-algebra and F-coalgebra T-algebra
Other uses Algebra Blessett, singer from the U.S. whose stage name is Algebra Algebra (book), a textbook by Serge Lang
See also Algebraic (disambiguation) List of all articles whose title begins with "algebra"