Generalized Derivations on Prime Near Rings
Let N be a near ring. An additive mapping f:N→N is said to be a right generalized (resp., left generalized) derivation with associated derivation d on N if f(xy)=f(x)y+xd(y) (resp., f(xy)=d(x)y+xf(y)) for all x,y∈N. A mapping f:N→N is said to be a generalized derivation with associated derivation d...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2013/170749 |
| Summary: | Let N be a near ring. An additive mapping f:N→N is said to be a
right generalized (resp., left generalized) derivation with associated derivation d on N if f(xy)=f(x)y+xd(y) (resp., f(xy)=d(x)y+xf(y)) for all x,y∈N. A mapping
f:N→N is said to be a generalized derivation with associated derivation d on N if
f is both a right generalized and a left generalized derivation with associated derivation
d on N. The purpose of the present paper is to prove some theorems in the setting of
a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby
extending some known results on derivations. |
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| ISSN: | 0161-1712 1687-0425 |