  This paper is devoted to the study of a fascinating class of residuated
lattices, the so-called mp-residuated lattice, in which any prime filter
contains a unique minimal prime filter. A combination of algebraic and
topological methods is applied to obtain new and structural results on
mp-residuated lattices. It is demonstrated that mp-residuated lattices are
strongly tied up with the dual hull-kernel topology. Especially, it is shown
that a residuated lattice is mp if and only if its minimal prime spectrum,
equipped with the dual hull-kernel topology, is Hausdorff if and only if its
prime spectrum, equipped with the dual hull-kernel topology, is normal. The
class of mp-residuated lattices is characterized by means of pure filters. It
is shown that a residuated lattice is mp if and only if its pure filters are
precisely its minimal prime filters, if and only if its pure spectrum is
homeomorphic to its minimal prime spectrum, equipped with the dual hull-kernel
topology.
