Annihilators of power values of b-generalized derivations in prime rings
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Date
2020-12-31
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi Fen Fakültesi
Abstract
Let
R
be a prime ring with extended centroid
C
and maximal left ring of quotients
Q
m
l
(
R
)
. For a nonzero element
b
∈
R
let
F
:
R
→
R
be a right generalized
b
-derivation associated with the map
d
of
R
. Suppose that
s
(
F
(
x
)
)
n
=
0
for all
x
∈
R
where
s
is a nonzero element in
R
and
n
≥
1
is a fixed positive integer. Then there exist some
c
∈
Q
m
l
(
R
)
and
β
∈
C
such that
d
(
x
)
=
a
d
c
(
x
)
,
F
(
x
)
=
(
b
+
β
)
x
b
for all
x
∈
R
and either
s
(
c
+
β
)
=
0
or
b
(
c
+
β
)
=
0
.
Description
Keywords
Prime ring, Generalized polynomial identity