  The notion of $n$-normal residuated lattice, as a class of residuated
lattices in which every prime filter contains at most $n$ minimal prime
filters, is introduced and studied. 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.
