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Residual lattice play an important role in the study of fuzzy logic based on t-norm. In this paper, we introduce the notions of Boolean filter in residual lattices, and therefore generalize the corresponding results which shown in BL-algebras by E. Turunen to residual lattices. We completely solve an open problem on filters of BL-algebras posed by M. Haveshki et al. Moreover, we investigate prime...