Let
R
R
be a ring. A formula
φ
(
x
)
\varphi ({\mathbf {x}})
in the language of left
R
R
-modules is called a positive primitive formula (ppf) if it is of the form
∃
y
(
A
B
)
(
x
y
)
=
0
\exists {\mathbf {y}}\left ({AB} \right )\left (\begin {array}{*{20}{c}}x\\y\\\end {array} \right ) = 0
where
A
A
and
B
B
are matrices of appropriate size with entries in
R
R
. We apply Prest’s notion of
D
φ
(
x
)
D\varphi ({\mathbf {x}})
, the ppf in the language of right
R
R
-modules dual to
φ
\varphi
, to show that the model theory of left
R
R
-modules as developed by Ziegler [Z] is in some sense dual to the model theory of right
R
R
-modules. We prove that the topologies on the left and right Ziegler spectra are "isomorphic" (Proposition 4.4). When the lattice of ppfs is well behaved, there is a homeomorphism
D
D
between the left and right Ziegler spectra which assigns to a given pure-injective indecomposable left
R
R
-module
U
U
the dual pure-injective indecomposable right
R
R
-module
D
U
DU
. Theorem 6.6 asserts that given a complete theory
T
T
of left
R
R
-modules, there is a dual complete theory
D
T
DT
of right
R
R
-modules with corresponding Baur-Garavaglia-Monk invariants. In the end, we give some conditions on a pure-injective indecomposable
R
U
_RU
which ensure that its dual
D
U
DU
may be represented as a hom set of the form
Hom
S
(
R
U
S
,
E
S
)
{\operatorname {Hom}_S}{(_R}{U_S},{E_S})
where
S
S
is some ring making
R
U
S
_R{U_S}
into a bimodule and
E
S
{E_S}
is injective.