Generalized state operators on residuated lattices
We give a definition of a generalized state operator (g-state operator) \(\sigma \) on a residuated lattice X and a g-state residuated lattice \((X,\sigma )\), by which the class of all g-state residuated lattices is proved to be a variety, and consider properties of g-state residuated lattices. We prove some fundamental results about them, such as characterizations of \(\sigma \)-filters, extended \(\sigma \)-filters, homomorphism theorems for g-state residuated lattices. Moreover, we show that every g-state residuated lattice is a subdirect product of subdirectly irreducible g-state residuated lattices.
Keywords(Generalized) state filters Extended filters Residuated lattices
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