\rightarrow \Omega_R^1 \otimes_R M$ such that $\nabla(rm) = dr \otimes m + r \cdot \nabla(m)$ for all $r \in R$ and $m \in M$. A connection $\nabla = \nabla^0$ on $M$ induces $k$-linear maps $\nabla^l: \Omega_R^l \otimes_R M \rightarrow \Omega_R^{l+1} \otimes_R M$ for all $l \geq 0$, where $\Omega_R^l$ is the $l$th exterior power of $\Omega_R^1$. If $\nabla^1 \circ \nabla^0$ is the zero map, the connection $\nabla$ is said to be *integrable*, in which case $\nabla^{l+1} \circ \nabla^l$ is the zero map for all $l$. Since ${\mathcal{D}}$ is generated over $R$ by derivations, the data of a left ${\mathcal{D}}$-module structure on an $R$-module $M$ is equivalent to that of an integrable connection on $M$ [@bjork 3.2.9], and the complex $(\Omega_R^{\bullet} \otimes_R M, \nabla^{\bullet})$ induced by $\nabla$ is the *de Rham complex* of $M$, which in coordinates $\{x_i\}$ is exactly the complex $M \otimes \Omega^{\bullet}_R$ defined above. The only use we will have in this paper for this alternate definition of $M \otimes \Omega^{\bullet}_R$ is the following obvious consequence:

\[dRind\] The de Rham cohomology spaces $H^i_{dR}(M)$ of any ${\mathcal{D}}$-module $M$ are independent of the choice of a regular system of parameters $x_1, \ldots, x_n$ for $R$.

There is a long exact 