Let
R
R
be a ring. A mapping
F
:
R
→
R
F:R \to R
is said to be commuting on
R
R
if
[
F
(
x
)
,
x
]
=
0
[F(x),x] = 0
holds for all
x
∈
R
x \in R
. The main purpose of this paper is to prove the following result, which generalizes a classical result of E. Posner: Let
R
R
be a prime ring of characteristic not two. Suppose there exists a nonzero derivation
D
:
R
→
R
D:R \to R
, such that the mapping
x
↦
[
D
(
x
)
,
x
]
x \mapsto [D(x),x]
is commuting on
R
R
. In this case
R
R
is commutative.