Let $A$ be a noetherian ring, and let $I\subseteq A$ be an ideal.
Suppose $I$ is generated by $a_1,\dots,a_n$.
Let $M$ be a left $A$-module.
If $A$ is commutative, then one can compute the derived $I$-torsion of $M$ by:
$H^n_I(M) \cong H^n(C(a_1,\dots,a_n)\otimes_A M)$, where $C(a_1,\dots,a_n)$ is the Cech complex associated to that sequence.
I would like to know if a similar result holds over non-commutative rings?
What are possible references for this?