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Abstract
A complete lattice (L, ≤) satisfying the infinite meet distributivity is called a frame. For a given bounded distributive lattice (X, ∧, ∨) and a frame L, we introduce the notions of prime L-fuzzy ideals and L-fuzzy prime ideals of X and prove certain characterization theorems for these. Using the duality principle in lattices, the results on prime L-fuzzy ideals and L-fuzzy prime ideals are extended for filters also
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Proof. Suppose that αI is a prime L-fuzzy ideal of X. Then αI is a proper and hence I is a proper ideal of X
and α ≠ 1. For any ideals J and K of X