Affiliation:
1. Department of Mathematics , Aligarh Muslim University , Aligarh 202002 , India
Abstract
Abstract
Consider
ℜ
{\Re}
as a prime ring which is non-commutative in structure with a suitable characteristic. Here,
𝒵
(
ℜ
)
{\mathcal{Z}(\Re)}
is the center of
ℜ
{\Re}
and
𝒬
{\mathcal{Q}}
is the Utumi ring of quotients where
𝒞
{\mathcal{C}}
is the extended centroid of
ℜ
{\Re}
. Suppose
𝒫
{\mathcal{P}}
to be a Lie ideal of
ℜ
{\Re}
which is non-central. Let
𝒦
{\mathcal{K}}
be a generalized derivation of
ℜ
{\Re}
related with derivation μ of
ℜ
{\Re}
. If
𝒦
{\mathcal{K}}
satisfies certain typical algebraic identities, then we prove that
𝒦
{\mathcal{K}}
is either the identity map or the zero map or the scalar map and further information is also drawn on the associated scalar unless
ℜ
{\Re}
embeds in
M
2
(
𝒞
)
{M_{2}(\mathcal{C})}
, a matrix ring of order
2
×
2
{2\times 2}
over
𝒞
{\mathcal{C}}
.
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