Abstract
Let
R
be a prime ring with center
Z
(
R
)
, right Martindale quotient ring
Q
and extended centroid
C
. By a
b
-generalized derivation we mean an additive mapping
g
:
R
→
Q
such that
g
(
x
y
)
=
g
(
x
)
y
+
b
x
d
(
y
)
for all
x
,
y
∈
R
, where
b
∈
Q
and
d
:
R
→
Q
is an additive map. In this paper, we extend some well-known results concerning (generalized) derivations on prime rings to
b
-generalized derivations. Further we investigate
b
-generalized derivation acting as a homomorphism or anti-homomorphism in a prime ring.
Publisher
Institute of Mathematics National Academy of Sciences of Ukraine
Subject
General Earth and Planetary Sciences,General Engineering,General Environmental Science
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