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Abstract
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The notion of $n$-normal residuated lattice, as a subclass of residuated lattices in which every prime filter contains at most $n$ minimal prime filters, is introduced and investigated. Before that, the notion of $\omega$-filter is introduced and it is observed that the set of $\omega$-filters in a residuated lattice forms a distributive lattice on its own, which includes the set of coannulets as a sublattice. The class of $n$-normal residuated lattices is characterized in terms of their prime filters, minimal prime filters, coannulets and $\omega$-filters. It is shown that a residuated lattice is normal if and only if its reticulation is conormal. Finally, the existence of the greatest $\omega$-filters contained in a given filter of a normal residuated lattice is obtained.
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