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

In this paper a particular case of $z$-ideals‎, ‎called {\it 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. ‎