Affiliation:
1. Department of Mathematics Faculty of Science King Abdulaziz University Rabigh Saudi Arabia - 21589
2. Department of Mathematics Faculty of Science & Arts-Rabigh King Abdulaziz University Rabigh Saudi Arabia
Abstract
Abstract
In this paper, it is shown that there is no positive integer n such that the set of
x
∈
A
$ x\in \mathfrak{A} $
for which
[
(
x
δ
)
n
,
(
x
∗
δ
)
n
(
x
δ
)
n
]
∈
Z
(
A
)
$ [(x^{\delta})^n, (x^{*{\delta}})^n(x^{\delta})^n]\in \mathcal{Z}(\mathfrak{A}) $
, where δ is a linear derivation on
A
$ \mathfrak{A} $
or there exists a central idempotent
e
∈
Q
$ e\in \mathcal{Q} $
such that δ=0 on
e
Q
$ e\mathcal{Q} $
and
(
1
−
e
)
Q
$ (1-e)\mathcal{Q} $
satisfies S
4(X
1, X
2, X
3, X
4). Moreover, we establish other related results.
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