By using the
v
v
-operation, a new characterization of the property for a power series ring to be a GCD domain is discussed. It is shown that if
D
D
is a
UFD
\operatorname {UFD}
, then
D\lBrack X\rBrack is a GCD domain if and only if for any two integral
v
v
-invertible
v
v
-ideals
I
I
and
J
J
of
D\lBrack X\rBrack such that
(
I
J
)
0
≠
(
0
)
,
(IJ)_{0}\neq (0),
we have
(
(
I
J
)
0
)
v
((IJ)_{0})_{v}
=
(
(
I
J
)
v
)
0
,
= ((IJ)_{v})_{0},
where
I
0
=
{
f
(
0
)
∣
f
∈
I
}
I_0=\{f(0) \mid f\in I\}
. This shows that if
D
D
is a GCD domain such that
D\lBrack X\rBrack is a
π
\pi
-domain, then
D\lBrack X\rBrack is a GCD domain.