It is shown that the graded ring
R
[
x
1
,
x
2
,
⋯
]
[
[
t
]
]
R[{x_1},{x_2}, \cdots ][[t]]
of homogeneous power series is a graded UFD if R is a regular UFD, the degrees of the
x
i
{x_i}
are positive and tend to
∞
\infty
, and t has degree
−
1
- 1
. In particular this applies to
M
U
∗
(
C
P
∞
)
M{U^ \ast }(C{P^\infty })
and
B
P
∗
(
C
P
∞
)
B{P^ \ast }(C{P^\infty })
.