  We introduce the notions of Strongly harmonic and Gelfand module, as a
generalization of the well-known ring theoretic case. We prove some properties
of these modules and we give a characterization via their lattice of submodules
and their space of maximal submodules. It is also observed that, under some
assumptions, the space of maximal submodules of a strongly harmonic module
constitutes a compact Hausdorff space whose frame of open sets is isomorphic to
the frame $\Psi(M)$ defined in [arXiv:1612.07407]. Finally, we mention some
open questions that arose during this investigation.
