Characterizations of Quantales by the Properties of their -Fuzzy (Subquantales) Ideals

Abstract

The notion of quantale, which designates a complete lattice equipped with an associative binary operation distributing over arbitrary joins, was used for the first time by Mulvey in 1986. In this paper, we present (α, β)-fuzzy (subquantales) ideals in quantales, where α, β may be one of these ∈γ, qδ, ∈γ ∨qδ and ∈γ ∧qδ. Special attension is considered to (∈γ, ∈γ ∨qδ)-fuzzy (subquantales) ideals. Some characterizations about (∈γ, ∈γ ∨qδ)-fuzzy prime and semi-prime ideals are also proved.