In this paper, we first show that for any space X, there is a Boolean subalgebra $mathcal{G}(z_X)$ of R(X) containg $mathcal{G}(X)$. Let X be a strongly zero-dimensional space such that $z_{eta}^{-1}(X)$ is the minimal cloz-coevr of X, where ($E_{cc}({eta}X)$, $z_{eta}$) is the minimal cloz-cover of ${eta}X$. We show that the minimal cloz-cover $E_{cc}(X)$ of X is a subspace of the Stone space $S(mathcal{G}(z_X))$ of $mathcal{G}(z_X)$ and that $E_{cc}(X)$ is a strongly zero-dimensional space if and only if ${eta}E_{cc}(X)$ and $S(mathcal{G}(z_X))$ are homeomorphic. Using these, we show that $E_{cc}(X)$ is a strongly zero-dimensional space and $mathcal{G}(z_X)=mathcal{G}(X)$ if and only if ${eta}E_{cc}(X)=E_{cc}({eta}X)$.