Summary: 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 \(z_\beta^{-1}(X)\) is the minimal cloz-cover of \(X\), where \((E_{cc}(\beta X),\, z_\beta)\) is the minimal cloz-cover of \(\beta X\). 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 \(\beta E_{cc}(X)\) 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 \(\beta E_{cc}(X)=E_{cc}(\beta X)\).