# Tensors in math and physics

I know how tensor product f two modules is defined in communtative algebra. But there is also a concept of tensors used in physics. Are these two concepts related? If yes, can someone explain me tensors as used in physics in terms of tensor product of two module?

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Yes, they are just tensor products of "physically meaningful" modules. –  Willie Wong Feb 13 at 16:49
I think physicists probably also use tensor fields on manifolds, which are slightly more general, in that they give you a tensor in a tensor power of the tangent space to the manifold at each point, but pointwise this is the same construction as above; each tangent space is a module over the base field (usually $\mathbb{R})$.