# ac.commutative algebra – Filtration over tensor product

Let
$$M supset M_1 supset ldots supset M_n supset ldots text{ and } N supset N_1 supset ldots supset N_n supset ldots$$
be exhaustive decreasing filtrations of modules over a commutative integral ring $$R$$. I would like to know if there is any way to define a filtration over $$M otimes_R N$$ such that the graduation $$Gr_k(M otimes_r N)$$ verifies
$$Gr_k(M otimes_r N)=oplus_{i+j=k} M_i/M_{i+1}otimes_RN_j/N_{j+1}.$$
I know it is possible to do so in the case of finite dimensional vector spaces by defining
$$(M otimes_R N)_k=sum_{i+j=k}M_i otimes N_j.$$
So if anyone has an idea or a reference where something like could be written, I would appreciate. Thanks for reading me.