Proper velocity Proper velocity In relativity, proper velocity, also known as celerity, is an alternative to velocity for measuring motion. Whereas velocity relative to an observer is distance per unit time where both distance and time are measured by the observer, proper velocity relative to an observer divides observer-measured distance by the time elapsed on the clocks of the traveling object. Proper velocity equals velocity at low speeds. Proper velocity at high speeds, moreover, retains many of the properties that velocity loses in relativity compared with Newtonian theory. For example, proper velocity equals momentum per unit mass at any speed, and therefore
Tensor product of modules "R" of "N". Then the tensor product of "M" and "N" over "R" can be defined as the coequalizer: together with the requirements If "S" is a subring of a ring "R", then formula_1 is the quotient group of formula_155 by the subgroup generated by formula_156, where formula_157 is the image of formula_158 under formula_159 In particular, any tensor product of "R"-modules can be constructed, if so desired, as a quotient of a tensor product of abelian groups by imposing the "R"-balanced product property. In the construction of the tensor product over a commutative ring "R", the "R"-module structure can