Completion of factor algebras of ideals

Let $\mathfrak{I}$ be a $\kappa$ -complete ideal over $\kappa$ . The structure of the completion of the Boolean algebra $\mathrm{\wp }(\kappa )/\mathfrak{I}$ is investigated with respect to properties of the ideal $\mathfrak{I}$ and the cardinal $\kappa$ . It is shown that under certain conditions $\mathrm{Comp}(\mathrm{\wp }(\kappa )/\mathfrak{I})$ is isomorphic to a collapse algebra.