‎pure ideals in residuated lattices

Ideals in mv algebras are‎, ‎by definition‎, ‎kernels of homomorphism‎. ‎an ideal is the dual of a filter in some special logical algebras but not in non-regular residuated lattices‎. ‎ideals in residuated lattices are defined as natural generalizations of ideals in mv algebras‎. ‎spec(l)‎, ‎the spectrum of a residuated lattice l‎, ‎is the set of all prime ideals of l‎, ‎and it can be endowed with the spectral topology‎. ‎the main scope of this paper is to characterize spec(l)‎, ‎called the stable topology‎. ‎in this paper‎, ‎we introduce and investigate the notion of pure ideal in residuated lattices‎, ‎and using these ideals we study the related spectral topologies‎.‎also‎, ‎using the model of mv algebras‎, ‎for a de morgan residuated lattice l‎, ‎we construct the belluce lattice associated with l‎. ‎this will provide information about the pure ideals and the prime ideals space of l‎. ‎so‎, ‎in this paper we generalize some results relative to mv algebras to the case of residuated lattices‎.