Characterizations of Quantales by the Properties of their (∈γ, ∈γ ∨qδ) - Fuzzy (Subquantales) Ideals

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 (alpha, beta)-fuzzy (subquantales) ideals in quantales, where alpha, beta may be one of these is an element of(gamma), q(delta), is an element of(gamma), boolean OR q(delta) and is an element of(gamma), boolean AND q(delta). Special attension is considered to (is an element of(gamma), is an element of(gamma) boolean OR q(delta) ),-fuzzy (subquantales) ideals. Some characterizations about (is an element of(gamma), is an element of(gamma) boolean OR q(delta))-fuzzy prime and semi -prime ideals are also proved.