$\mathcal I$-IDEALS GENERATED BY A SET IN IS-ALGEBRAS
Young-Bae Jun, Eun-Hwan Roh, Xiaolong Xin · Bulletin of the Korean Mathematical Society · 1998
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)-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 -ideal in an IS-algebra, and show that in a finite IS-algebra, every -ideal is closed.