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Abstract
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In this paper we introduce and investigate the notions of coannihilators and coannulets of a residuated
lattice. Following standard methods, we obtain that, given a residuated lattice A and a filter F of A,
the complete lattice P(A) is F -pseudocomplemented and that the set ?F (A) of F -coannihilators can be
endowed with a structure of complete Boolean lattice. We show that the set ?F (A) of F -coannulets, the
coannihilator of singletons, is a sublattice of ?F (A). Finally, we characterize coannihilators in terms of
minimal prime filters and we give a sufficient condition for a residuated lattice to be hyperarchimedean.
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