Jump to content

Algebra (disambiguation)

From Wikipedia, the free encyclopedia

The word 'algebra' is used for various branches and structures of mathematics. For their overview, see Algebra.

The bare word "algebra"

[edit]

The bare word "algebra" may refer to:

In universal algebra, algebra has an axiomatic definition, roughly as an instance of any of a number of algebraic structures, such as groups, rings, etc.

Branches of mathematics

[edit]

The term is also traditionally used for the field of:

  • Computer algebra, dealing with software systems for symbolic mathematical computation, which often offer capabilities beyond what is normally understood to be "algebra"

Mathematical structures

[edit]

Vector space with multiplication

[edit]

An "algebra", or to be verbose, an algebra over a field, is a vector space equipped with a bilinear vector product. Some notable algebras in this sense are:

See also coalgebra, the dual notion.

Other structures

[edit]

A different class of "algebras" consists of objects which generalize logical connectives, sets, and lattices.

"Algebra" can also describe more general structures:

Other uses

[edit]

See also

[edit]