A nonassociative ring is called a derivation alternator ring if it satisfies the identities
(
y
z
,
x
,
x
)
=
y
(
z
,
x
,
x
)
+
(
y
,
x
,
x
)
z
,
(
x
,
x
,
y
z
)
=
y
(
x
,
x
,
z
)
+
(
x
,
x
,
y
)
z
(yz,\,x,\,x)\, = \,y(z,\,x,\,x)\, + \,(y,\,x,\,x)z,\,(x,\,x,\,yz)\, = \,y(x,\,x,\,z)\, + \,(x,\,x,\,y)z
and
(
x
,
x
,
x
)
=
0
(x,\,x,\,x)\, = 0
. Let R be a prime derivation alternator ring with idempotent
e
≠
1
e \ne 1
and characteristic
≠
2
\ne 2
. If R is without nonzero nil ideals of index 2, then R is alternative.