for extension of scalars. For a commutative ring, the tensor product of modules can be iterated to form the tensor algebra of a module, allowing one to...

v\otimes w} is called the tensor product of v and w. An element of V ⊗ W {\displaystyle V\otimes W} is a tensor, and the tensor product of two vectors is sometimes...

product) Tensor product of modules, the same operation slightly generalized to modules over arbitrary rings Kronecker product, the tensor product of matrices...

as R-modules, their tensor product A ⊗ R B {\displaystyle A\otimes _{R}B} is also an R-module. The tensor product can be given the structure of a ring...

derived tensor product of M and N. In particular, π 0 ( M ⊗ R L N ) {\displaystyle \pi _{0}(M\otimes _{R}^{L}N)} is the usual tensor product of modules M and...

are O-modules, then their tensor product, denoted by F ⊗ O G {\displaystyle F\otimes _{O}G} or F ⊗ G {\displaystyle F\otimes G} , is the O-module that...

One-form Tensor product of modules Application of tensor theory in engineering Continuum mechanics Covariant derivative Curvature Diffusion tensor MRI Einstein...

the derived functors of the tensor product of modules over a ring. Along with the Ext functor, Tor is one of the central concepts of homological algebra...

definition of tensor products of modules. The set of submodules of a given module M, together with the two binary operations + (the module spanned by...

a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space or manifold) or of the...