A Dual Zariski Topology for Modules

We introduce a dual Zariski topology on the spectrum of fully coprime $R$-submodules of a given duo module $M$ over an associative (not necessarily commutative) ring $R$. This topology is defined in a way dual to that of defining the Zariski topology on the prime spectrum of $R$. We investigate this topology and clarify the interplay between the properties of this space and the algebraic properties of the module under consideration.