On v-filters and normal v-filters of a residuated lattice with a weak vt-operator

In this paper, we study further the filter theory of residuated lattices. First, we discuss the concepts of filters and normal filters of residuated lattices and propose some equivalent conditions for them. Then we introduce and investigate the notions of v-filter and normal v-filter of a residuated lattice with a weak vt-operator and lay bare the formulas for calculating the v-filters and the normal v-filters generated by subsets. Finally we show that the lattices of v-filters and normal v-filters of a residuated lattice with a vt-operator are both complete Brouwerian lattices.