Affiliation:
1. Department of Mathematics , Aligarh Muslim University , Aligarh - 202002 India
2. Faculty of Science & Arts-Rabigh , King Abdulaziz University , Jeddah , Saudi Arabia
Abstract
Abstract
Let
ℛ
{\mathscr{R}}
be a prime ring,
𝒬
r
{\mathscr{Q}_{r}}
the right Martindale quotient ring of
ℛ
{\mathscr{R}}
and
𝒞
{\mathscr{C}}
the extended centroid of
ℛ
{\mathscr{R}}
.
In this paper, we discuss the relationship between the structure of prime rings and the behavior of skew derivations on multilinear polynomials. More precisely, we investigate the m-potent commutators of skew derivations involving multilinear polynomials, i.e.,
(
[
δ
(
f
(
x
1
,
…
,
x
n
)
)
,
f
(
x
1
,
…
,
x
n
)
]
)
m
=
[
δ
(
f
(
x
1
,
…
,
x
n
)
)
,
f
(
x
1
,
…
,
x
n
)
]
,
\big{(}[\delta(f(x_{1},\ldots,x_{n})),f(x_{1},\ldots,x_{n})]\big{)}^{m}=[%
\delta(f(x_{1},\ldots,x_{n})),f(x_{1},\ldots,x_{n})],
where
1
<
m
∈
ℤ
+
{1<m\in\mathbb{Z}^{+}}
,
f
(
x
1
,
x
2
,
…
,
x
n
)
{f(x_{1},x_{2},\ldots,x_{n})}
is a non-central multilinear polynomial over
𝒞
{\mathscr{C}}
and δ is a skew derivation of
ℛ
{\mathscr{R}}
.
Cited by
1 articles.
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