The Characterizations of Tensor Product Functors and Their Derived Functors of Left Modules

In 1979, Zhou Boxun introduced concepts of the tensor product of left modules, so that there exist tensor products of left modules which is an extension of the tensor products of modules over commutative rings. In 2], it was proved that - M preserves direct limits and (-M, Horn(M, -)) is an adjoint pair.In this paper, we characterize functor -M and its derived functors. These results can be consider as extensions of Watts′theorems