For a multiplication
![$R$](img7.png)
-module
![$M$](img8.png)
we define the primitive topology
![$\mathcal{T} $](img9.png)
on the set
![$Prt\left( M\right) $](img10.png)
of primitive
submodules of
![$M$](img8.png)
. We prove that if
![$R$](img7.png)
is a commutative ring and
![$M$](img8.png)
is a multiplication
![$R$](img7.png)
-module, then the complete lattice
![$Sprt\left( M\right) $](img11.png)
of semiprimitive submodules of
![$M$](img8.png)
is a
spatial frame. When
![$M$](img8.png)
is projective in the category
![$\sigma [M]$](img12.png)
,
we obtain that the topological spaces
![$(Prt(M),\mathcal{T} $](img13.png)
) and
![$(Prt(R),\mathcal{T} $](img14.png)
) are homeomorphic. As an application, we
prove that if
![$M$](img8.png)
is projective in the category
![$\sigma [M]$](img12.png)
, then
![$Prt(R)$](img15.png)
has classical Krull dimension if and only if
![$Prt(M)$](img16.png)
has
classical Krull dimension.