  The goal of this paper is to deepen the study of multiplicative lattices in
the sense of Facchini, Finocchiaro and Janelidze. We provide a sort of Prime
Ideal Principle that guarantees that maximal implies prime in a variety of
cases (among them the case of commutative rings with identity). This result is
used to study the lattice theoretic counterpart of multiplicative closed sets,
that of m-systems. The notion of m-system is also studied from the topological
point of view.
