The aim of this paper is to develop the spectral theory of prime L-ideals in ordered semigroups. Firstly the concepts of an L-fuzzy ideal and that of an L-fuzzy prime ideal are given and discussed. And then a topological space, called the L-fuzzy prime spectrum of an ordered semigroup, has been gained. This topological space is T1 and sober. Furthermore some homeomorphic spaces of this topological space are investigated. Finally, a contravariant functor from the category of commutative ordered semigroups into the category of sober topological spaces is obtained.
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