Fuzzy Spectral Spaces and Fuzzy Congruences of a Heyting ADL

Abstract

In this paper, the space F p of fuzzy prime ideals of Heyting almost distributive lattice H is studied, and it is shown that the collection of all sets M η is a topology on F p , where η is a fuzzy ideal on H and M η = θ ∈ F p | η ⊈ θ . The only compact subset of the space F p is given. A fuzzy congruence relation Θ on H is defined, and the homomorphism between the set of all fuzzy ideals of H and the set of all fuzzy ideals of H / Θ is established. Furthermore, we established an isomorphism between fuzzy spectrum of H and fuzzy spectrum of H / Θ .