Resumen de Simple, local and subdirectly irreducible state residuated lattices

M. Taheri, F. Khaksar Haghani, S. Rasouli

• 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.