The exercise 9.9.5 of Weibel's homological algebra states that
$\textbf{Exercises 9.9.5}$ If $Z$ is a nilpotent ideal of $R$ and $k$ is a field of $char(k) = 0$, show that $H_{dR}^{\ast}(R) \cong H_{dR}^{\ast}(R/I)$.
where $R$ is commutative positively graded $k$-algebra. Here, I don't understand what is $Z$? He used the $Z(R)$ to denote the cyclic module associated to ring $R$, but which is nilpotent does not make sense. So what I am understanding is that this $Z$ should be $I$ in above exercise. But in that case exercise becomes:
$\textbf{Exercises}$ If $I$ is a nilpotent ideal of $R$ and $k$ is a field of $char(k) = 0$, show that $H_{dR}^{\ast}(R) \cong H_{dR}^{\ast}(R/I)$.
which looks very suspicious. Even though this is true when we replace $H^{\ast}_{dR}$ by periodic cycle homology $HC^{per}_{\ast}$ but for de Rham cohomology it seems very odd. Can someone clear this confusion whether this is typo error (Z instead of I) or the original exercise really mean something else.
