سعید رسولی

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.