Algebra (disambiguation)

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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]