Affiliation:
1. Department of Mathematics , Aligarh Muslim University , Aligarh 202002 , India
Abstract
Abstract
Let R be an associative ring. A multiplicative semi-derivation d is a map on R satisfying
d
(
x
y
)
=
d
(
x
)
g
(
y
)
+
x
d
(
y
)
=
d
(
x
)
y
+
g
(
x
)
d
(
y
)
and
d
(
g
(
x
)
)
=
g
(
d
(
x
)
)
{d(xy)=d(x)g(y)+xd(y)=d(x)y+g(x)d(y)\quad\text{and}\quad d(g(x))=g(d(x))}
for all
x
,
y
∈
R
{x,y\in R}
, where g is any map on R. In this paper, we have obtained some conditions on R, which make d additive. Finally, we have also shown that every multiplicative semi-derivation on
M
n
(
ℂ
)
{M_{n}(\mathbb{C})}
, the algebra of all
n
×
n
{n\times n}
matrices over the field
ℂ
{\mathbb{C}}
of complex numbers, is an additive derivation.
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*
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Cited by
2 articles.
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