On Generalized Semiderivations of Prime Near Rings
Let N be a near ring. An additive mapping F:N→N is said to be a generalized semiderivation on N if there exists a semiderivation d:N→N associated with a function g:N→N such that F(xy)=F(x)y+g(x)d(y)=d(x)g(y)+xF(y) and F(g(x))=g(F(x)) for all x,y∈N. In this paper we prove that prime near rings satisf...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2015/867923 |
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| author | Abdelkarim Boua A. Raji Asma Ali Farhat Ali |
| author_facet | Abdelkarim Boua A. Raji Asma Ali Farhat Ali |
| author_sort | Abdelkarim Boua |
| collection | DOAJ |
| description | Let N be a near ring. An additive mapping F:N→N is said to be a generalized semiderivation on N if there exists a semiderivation d:N→N associated with a function g:N→N such that F(xy)=F(x)y+g(x)d(y)=d(x)g(y)+xF(y) and F(g(x))=g(F(x)) for all x,y∈N. In this paper we prove that prime near rings satisfying identities involving semiderivations are commutative rings, thereby extending some known results on derivations, semiderivations, and generalized derivations. We also prove that there exist no nontrivial generalized semiderivations which act as a homomorphism or as an antihomomorphism on a 3-prime near ring N. |
| format | Article |
| id | doaj-art-e0d4a2807c5e4236a68d0a5dcf24882c |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e0d4a2807c5e4236a68d0a5dcf24882c2025-08-20T02:21:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252015-01-01201510.1155/2015/867923867923On Generalized Semiderivations of Prime Near RingsAbdelkarim Boua0A. Raji1Asma Ali2Farhat Ali3Department of Mathematics, Faculty of Sciences of Agadir, Ibn Zohr University, P.O. Box 8106, Agadir, MoroccoDépartement de Mathématiques, Faculté des Sciences et Techniques, Université Moulay Ismaïl, Groupe d’Algèbre et Applications, BP 509, Boutalamine, Errachidia, MoroccoDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaLet N be a near ring. An additive mapping F:N→N is said to be a generalized semiderivation on N if there exists a semiderivation d:N→N associated with a function g:N→N such that F(xy)=F(x)y+g(x)d(y)=d(x)g(y)+xF(y) and F(g(x))=g(F(x)) for all x,y∈N. In this paper we prove that prime near rings satisfying identities involving semiderivations are commutative rings, thereby extending some known results on derivations, semiderivations, and generalized derivations. We also prove that there exist no nontrivial generalized semiderivations which act as a homomorphism or as an antihomomorphism on a 3-prime near ring N.http://dx.doi.org/10.1155/2015/867923 |
| spellingShingle | Abdelkarim Boua A. Raji Asma Ali Farhat Ali On Generalized Semiderivations of Prime Near Rings International Journal of Mathematics and Mathematical Sciences |
| title | On Generalized Semiderivations of Prime Near Rings |
| title_full | On Generalized Semiderivations of Prime Near Rings |
| title_fullStr | On Generalized Semiderivations of Prime Near Rings |
| title_full_unstemmed | On Generalized Semiderivations of Prime Near Rings |
| title_short | On Generalized Semiderivations of Prime Near Rings |
| title_sort | on generalized semiderivations of prime near rings |
| url | http://dx.doi.org/10.1155/2015/867923 |
| work_keys_str_mv | AT abdelkarimboua ongeneralizedsemiderivationsofprimenearrings AT araji ongeneralizedsemiderivationsofprimenearrings AT asmaali ongeneralizedsemiderivationsofprimenearrings AT farhatali ongeneralizedsemiderivationsofprimenearrings |