In a recent paper [1] Gupta proved that a division ring satisfying the polynomial identity
x
y
2
x
=
y
x
2
y
x{y^2}x = y{x^2}y
is commutative. In this note our goal is to prove the following: If
R
R
is a semiprime ring with
x
y
2
x
−
y
x
2
y
x{y^2}x - y{x^2}y
central in
R
R
, for all
x
,
y
x,y
in
R
R
, then
R
R
is commutative.