Wikipedia: History of Algebra

Difference (from prior major revision) (author diff)

Changed: 7c7

An algebra over a field (or simply an algebra) is a vector space A together with a vector multiplication that distributes over vector addition and has the further property that (ax)(by) = (ab)(xy) for all scalars a and b and all vectors x and y. Such a vector multiplication is a [bilinear map]? A x A -> A. The most important types of algebras are the associative algebras, such as algebras of matrices or polynomials, and the Lie algebras, such as R³ with the multiplication given by the vector cross product or algebras of [vector fields]?.

An algebra over a field (or simply an algebra) is a vector space A together with a vector multiplication that distributes over vector addition and has the further property that (ax)(by) = (ab)(xy) for all scalars a and b and all vectors x and y. Such a vector multiplication is a bilinear map A x A -> A. The most important types of algebras are the associative algebras, such as algebras of matrices or polynomials, and the Lie algebras, such as R³ with the multiplication given by the vector cross product or algebras of [vector fields]?.

	Revision 10 . . November 21, 2001 1:45 am by AxelBoldt [link to associative and Lie algebras]
	Revision 9 . . November 21, 2001 1:44 am by AxelBoldt [link to associative and Lie algebras]
	Revision 8 . . November 8, 2001 11:38 pm by AxelBoldt [linear algebra link]
	Revision 7 . . September 4, 2001 3:33 am by Zundark [moving some stuff to another page]