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Abstract
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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.
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