ZERO ELEMENTS AND z-IDEALS IN MODIFIED POINTFREE TOPOLOGY

‎In this paper‎, ‎we define and study the notion of zero elements in topoframes; a topoframe is a pair‎ ‎(L‎,‎τ)‎, ‎abbreviated Lτ‎, ‎consisting of a frame L and a‎ ‎subframe τ all of whose elements are complemented elements in‎ ‎L‎. ‎We show that‎ ‎the f-ring R(Lτ)‎, ‎the set of τ-real continuous functions on L‎, ‎is uniformly complete‎. ‎Also‎, ‎the set of all zero elements in a topoframe‎ ‎is closed under the formation of countable meets and finite joins‎. ‎Also‎, ‎we introduce the notion of z-filters and z-ideals in modified pointfree topology‎ ‎and make ready some results about them‎.