$\mathcal I$-IDEALS GENERATED BY A SET IN IS-ALGEBRAS

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.