Saeed Rasoli

The aim of this paper is to extend the notion of the generalized co-annihilator of residuated lattices. We introduce the concept of a generalized co-annihilator of a given subset of a residuated lattice A. We prove that generalized co-annihilators relative to a filter F of A are again filters, and moreover pseudocomplements in the lattice Fi(A)[F, A] of all filters of A containing F. Also, for a given filter F of A we prove that the set Co ? AnF (A) of all generalized co-annihilators relative to F forms a complete Boolean lattice.