Let $A$ be a commutative unital $k$-algebra. Then we have de Rham complex given as: $C_{\ast}(A)$ : $ 0 \rightarrow A \rightarrow \Omega_{A \lvert k}^{1} \rightarrow \Omega_{A \lvert k}^{2} \rightarrow ... $ and de Rham Cohomology group $H_{dR}^{\ast}(A \lvert k)$ is defined as the cohomology group of this complex. I want to know is there a definition of relative de Rham cohomology groups($H_{dR}^{\ast}(A\lvert k, I))$ of $A$ with respect to some ideal $I$? I don't know any reference of this definition. I need this notion because I want to relate these groups with the relative cyclic homology groups $HC_{\ast}(A\lvert k, I)$.

I am guessing that these groups is defined as the cohomology group of complex $C_{\ast}(A, I)$, where the complex $C_{\ast}(A, I)$ is defined by the following exact sequence of complex. $ 0 \rightarrow C_{\ast}(A, I) \rightarrow C_{\ast}(A) \rightarrow C_{\ast}(A/I)$. Tell me whether my guess is correct or not. It would be great if someone can give reference for this literature?


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