  Given a duo module $M$ over an associative (not necessarily commutative) ring
$R,$ a Zariski topology is defined on the spectrum
$\mathrm{Spec}^{\mathrm{fp}}(M)$ 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.
