If "R" is not commutative, the order of tensor products could matter in the following way: we "use up" the right action of "M" and the left action of "N" to form the tensor product formula_2; in particular, formula_87 would not even be defined. If "M", "N" are bi-modules, then formula_2 has the left action coming from the left action of "M" and the right action coming from the right action of "N"; those actions need not be the same as the left and right actions of formula_87.