The structure of the W^(*)--tensor product over a W^(*)--subalgebra and its predual (σ--finite case)

Let $M$, $N$, $R$ be $W^{*}$--algebras, with $R$ unitally embedded in both $M$ and $N$. by using Reduction Theory, we extend the previous description of the $W^{*}$--tensor product $M\bar\otimes_{R}N$ over the common $W^{*}$--subalgebra $R$ and its predual $(M\bar\otimes_{R}N)_{*}$ to the $\sigma$--finite case.