Mass (say) 1 kilogram. Then we can measure the mass of any other object in the universe by colliding it with the reference object and measuring the accelerations. Additionally, mass relates a body's momentum p to its linear velocity v: and the body's kinetic energy "K" to its velocity: The primary difficulty with Mach's definition of mass is that it fails to take into account the potential energy (or binding energy) needed to bring two masses sufficiently close to one another to perform the measurement of mass. This is most vividly demonstrated by comparing the mass of the proton in the
Tensor product of modules in its right argument: In the general case, each element of the tensor product of modules gives rise to a left "R"-linear map, to a right "R"-linear map, and to an "R"-bilinear form. Unlike the commutative case, in the general case the tensor product is not an "R"-module, and thus does not support scalar multiplication. Both cases hold for general modules, and become isomorphisms if the modules "E" and "F" are restricted to being finitely generated projective modules (in particular free modules of finite ranks). Thus, an element of a tensor product of modules over a ring "R" maps canonically