Книга: Tensor Algebra: Mathematics, Vector Space, Algebra Over a Field, Tensor, Free Algebra, Associative Algebra, Direct Sum of Modules, Free Object, Commutative Diagram, Quotient Ring, Exterior Algebra

High Quality Content by WIKIPEDIA articles! In mathematics, the tensor algebra of a vector space V, denoted T(V) or T?(V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product. It is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the 'most general' algebra containing V, in the sense of the corresponding universal property. The tensor algebra also has a coalgebra structure.