Author:
Bera Nripendu,Dhara Basudeb
Abstract
UDC 512.5
Suppose that
R
is a prime ring with
c
h
a
r
(
R
)
≠
2
and
f
(
ξ
1
,
…
,
ξ
n
)
is a noncentral multilinear polynomial over
C
(
=
Z
(
U
)
)
,
where
U
is the Utumi quotient ring of
R
.
An additive mapping
h
:
R
→
R
is called homoderivation if
h
(
a
b
)
=
h
(
a
)
h
(
b
)
+
h
(
a
)
b
+
a
h
(
b
)
for all
a
,
b
∈
R
.
We investigate the behavior of three generalized derivations
F
,
G
,
and
H
of
R
satisfying the condition
F
(
ξ
2
)
=
G
(
ξ
)
2
+
H
(
ξ
)
ξ
+
ξ
H
(
ξ
)
for all
ξ
inf
(
R
)
=
{
f
(
ξ
1
,
…
,
ξ
n
)
∣
ξ
1
,
…
,
ξ
n
∈
R
}
.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Subject
General Earth and Planetary Sciences,General Engineering,General Environmental Science
Reference23 articles.
1. E. Albas, Generalized derivations on ideals of prime rings, Miskolc Math. Notes, 14, № 1, 3–9 (2013).
2. E. F. Alharfie, N. M. Muthana, On homoderivations and commutativity of rings, Bull. Inst. Math. Virtual Inst., 9, 301–304 (2019).
3. E. F. Alharfie, N. M. Muthana, The commutativity of prime rings with homoderivations, Int. J. Adv. and Appl. Sci., 5, № 5, 79–81 (2018).
4. A. Al-Kenani, A. Melaibari, N. Muthana, Homoderivations and commutativity of $ast$-prime rings, East-West J. Math., 17, № 2, 117–126 (2015).
5. A. Ali, N. Rehman, S. Ali, On Lie ideals with derivations as homomorphisms and antihomomorphisms, Acta Math. Hungar., 101, № 1-2, 79–82 (2003).