Boolean Filters and Prime Filters of Residual Lattices

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 filters of residuated lattices, and by using the software MATHEMATICA, we also give a counterexample to show the distinction between prime filters of residual lattices and one of MTL-algebras.