In this paper, we first show that for any space X, there is a ${sigma}$-complete Boolean subalgebra of $mathcal{R}$(X) and that the subspace {${alpha}{mid}{alpha}$ is a fixed ${sigma}Z(X)^{sharp}$-ultrafilter} of the Stone-space $S(Z({Lambda}_X)^{sharp})$ is the minimal basically disconnected cover of X. Using this, we will show that for any countably locally weakly Lindel$ddot{o}$f space X, the set {$M{mid}M$ is a ${sigma}$-complete Boolean subalgebra of $mathcal{R}$(X) containing $Z(X)^{sharp}$ and $s_M^{-1}(X)$ is basically disconnected}, when partially ordered by inclusion, becomes a complete lattice.