We consider a generalization of [1. theorem 2.5]. We give a description of the element of $_{mathcal I}^l$(resp. $_{mathcal I} ^r$), where A and B are left (resp. right)${mathcal I}$-ideals of an IS-algebra X. For a nonempty left (resp. right) stable, we obtain a condition for $_{mathcal I}^l$(resp. $_{mathcal I}^l$) to be closed. We give a characterization of a closed $mathcal I$-ideal in an IS-algebra, and show that in a finite IS-algebra, every $mathcal I$-ideal is closed.