Algebra may refer to:
Branches of mathematics
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.
"Algebra" can also describe more general structures:
Other uses
See also