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Algebra (disambiguation)

Topics referred to by the same term From Wikipedia, the free encyclopedia

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The word 'algebra' is used for various branches and structures of mathematics. For their overview, see Algebra. The name comes from the famous 10th century book Al-Jabr by Al-Khwarizmi.

The bare word "algebra"

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

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

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Vector space with multiplication

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

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

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