In this paper we study the structure of a right Noetherian ring
R
R
of finite right global dimesion integral over a central subring
C
C
and satisfying the following condition: if
V
,
W
V,W
are irreducible right
R
R
-modules with
r
C
(
V
)
=
r
C
(
W
)
{r_C}(V) = {r_C}(W)
then
pr
dim
(
V
)
=
pr
dim
(
W
)
\operatorname {pr}\, \dim (V) = \operatorname {pr}\, \dim (W)
.