A Zariski Topology for Modules

Given a duo module $M$ over an associative (not necessarily commutative) ring $R,$ a Zariski topology is defined on the spectrum ${\mathrm{S}\mathrm{p}\mathrm{e}\mathrm{c}}^{\mathrm{f}\mathrm{p}}(M)$ of {\it fully prime} $R$-submodules of $M$. We investigate, in particular, the interplay between the properties of this space and the algebraic properties of the module under consideration.