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...
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| Format: | Article |
| Language: | English |
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Wiley
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 |
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| author | Asma Ali Howard E. Bell Phool Miyan |
| author_facet | Asma Ali Howard E. Bell Phool Miyan |
| author_sort | Asma Ali |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ac560109254c4a088fcfe37c484ccf07 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ac560109254c4a088fcfe37c484ccf072025-02-03T01:01:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252013-01-01201310.1155/2013/170749170749Generalized Derivations on Prime Near RingsAsma Ali0Howard E. Bell1Phool Miyan2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Brock University, St. Catharines, ON, L2S 3A1, CanadaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaLet 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.http://dx.doi.org/10.1155/2013/170749 |
| spellingShingle | Asma Ali Howard E. Bell Phool Miyan Generalized Derivations on Prime Near Rings International Journal of Mathematics and Mathematical Sciences |
| title | Generalized Derivations on Prime Near Rings |
| title_full | Generalized Derivations on Prime Near Rings |
| title_fullStr | Generalized Derivations on Prime Near Rings |
| title_full_unstemmed | Generalized Derivations on Prime Near Rings |
| title_short | Generalized Derivations on Prime Near Rings |
| title_sort | generalized derivations on prime near rings |
| url | http://dx.doi.org/10.1155/2013/170749 |
| work_keys_str_mv | AT asmaali generalizedderivationsonprimenearrings AT howardebell generalizedderivationsonprimenearrings AT phoolmiyan generalizedderivationsonprimenearrings |