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Abstract
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This paper is devoted to investigating the notions of simple, local and subdirectly irreducible state residuated lattices and some of their related properties. The filters generated by a subset in state residuated lattices are characterized and it is shown that the lattice of filters of a state residuated lattice forms a complete Heyting algebra. Maximal, prime and minimal prime filters of a state residuated lattice are investigated and it is shown that any filter of a state residuated lattice contains a minimal prime filter. Finally, the relevant notions are discussed and characterized.
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