Tensor product of gamma modules

Let R be a Γ-ring and M, N be a right RΓ-module and a left RΓ-module respectively. We construct the abelian group M⊗RΓN and show that this abelian group is an RΓ-module if R is a commutative Γ-ring. Then, we study some properties of this type of tensor product and α-free RΓ-modules. Moreover, we show that there are many differences between tensor product of modules and RΓ-modules. © 2014, African Mathematical Union and Springer-Verlag Berlin Heidelberg.