zero sets in pointfree topology and strongly $z$-ideals

in this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. we study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. for strongly z-ideals, we analyze prime ideals using the concept of zero sets. moreover, it is proven that the intersection of all zero sets of a prime ideal of c(l), which is ring of real-valued continuous functions for frame l, does not have more than one element. also, z-filters are introduced in terms of pointfree topology. then the relationship between z-filters and ideals, particularly maximal ideals, is examined. finally, it is shown that the family of all zero sets is a base for the collection of closed sets.