Closure Ideals of $MS$-Algebras

The concepts of dominator ideals and closure ideals are introduced in $MS$-algebras and many properties of these ideals are studied. Closure ideals are characterized in terms of principal dominator ideals. It is then proved that the lattice of all closure ideals is isomorphic to the ideal lattice of the lattice of all principal dominator ideals. A set of equivalent conditions is obtained to characterize closure ideals of $MS$-algebras. Finally some properties of closure ideals are studied with respect to homomorphisms.