IfAnalogously, if ''N'' has a right action by a ring ''S'', then, in the analogous way, <math>M \otimes_R N</math> becomes a right ''S''-module.<!-- Doesn't seem correct; see the example below. Strictly speaking, the ring used to form the tensor should be indicated: most modules can be considered as modules over several different rings or over the same ring with a different actions of the ring on the module elements. For example, it can be shown that {{nowrap|'''R''' ⊗<sub>'''R'''</sub> '''R'''}} and {{nowrap|'''R''' ⊗<sub>'''Z'''</sub> '''R'''}} are completely different from each other. However in practice, whenever the ring is clear from context, the subscript denoting the ring may be dropped.-->
===Tensor product of linear maps and a change of base ring===
