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In this paper the concept of prime L-fuzzy ideals and L-fuzzy prime ideals of an ADL A with truth values in a complete lattice L satisfying the infinite meet distributive law are introduced. All prime L-fuzzy ideals of a given ADL A are determined by establishing a one-to-one correspondence between prime L-fuzzy ideals of an ADL A and the pairs (P, α), where P is a prime ideal of A and α is a prime element in L. Also, here minimal prime L-fuzzy ideals and L-fuzzy minimal prime ideals of an ADL A are introduced and characterized.

The notion of an Almost Distributive Lattice (ADL) is a common abstraction of several lattice theoretic and ring theoretic generalizations of Boolean algebra and Boolean rings. In this paper, the set of all L -fuzzy prime ideals of an ADL with truth values in a complete lattice L satisfying the infinite meet distributive law is topologized and the resulting space is discussed.

In this paper, we introduce the concept of an [Formula: see text]-pseudo complementation [Formula: see text] on an Almost Distributive Lattice [Formula: see text] for an arbitrary fixed element [Formula: see text] and any [Formula: see text] of [Formula: see text] and discuss several properties of this. Here, we obtain a bijection correspondence between the [Formula: see text]-pseudo complementations on [Formula: see text] and maximal elements of [Formula: see text] We prove that the set [Formula: see text] is a Boolean algebra which is independent(upto isomorphism) of the [Formula: see text]-pseudo complementation [Formula: see text].

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