6 research outputs found
Some properties of state filters in state residuated lattices
summary:We consider properties of state filters of state residuated lattices and prove that for every state filter of a state residuated lattice : \begin {itemize} \item [(1)] is obstinate ; \item [(2)] is primary is a state local residuated lattice; \end {itemize} and that every g-state residuated lattice is a subdirect product of , where is a prime state filter of . \endgraf Moreover, we show that the quotient MTL-algebra of a state residuated lattice by a state prime filter is not always totally ordered, although the quotient MTL-algebra by a prime filter is totally ordered