Generalized Derivations in Semiprime Gamma Rings
Let M be a 2-torsion-free semiprime Γ-ring satisfying the condition aαbβc=aβbαc for all a,b,c∈M, α,β∈Γ, and let D:M→M be an additive mapping such that D(xαx)=D(x)αx+xαd(x) for all x∈M, α∈Γ and for some derivation d of M. We prove that D is a generalized derivation.
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/270132 |
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| _version_ | 1832566418262982656 |
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| author | Kalyan Kumar Dey Akhil Chandra Paul Isamiddin S. Rakhimov |
| author_facet | Kalyan Kumar Dey Akhil Chandra Paul Isamiddin S. Rakhimov |
| author_sort | Kalyan Kumar Dey |
| collection | DOAJ |
| description | Let M be a 2-torsion-free semiprime Γ-ring satisfying the condition aαbβc=aβbαc for all a,b,c∈M, α,β∈Γ, and let D:M→M be an additive mapping such that D(xαx)=D(x)αx+xαd(x) for all x∈M, α∈Γ and for some derivation d of M. We prove that D is a generalized derivation. |
| format | Article |
| id | doaj-art-8914d76f44694741ac1314c60078dee9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8914d76f44694741ac1314c60078dee92025-02-03T01:04:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/270132270132Generalized Derivations in Semiprime Gamma RingsKalyan Kumar Dey0Akhil Chandra Paul1Isamiddin S. Rakhimov2Department of Mathematics, University of Rajshahi, Rajshahi 6205, BangladeshDepartment of Mathematics, University of Rajshahi, Rajshahi 6205, BangladeshDepartment of Mathematics, FS, and Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 Serdang, MalaysiaLet M be a 2-torsion-free semiprime Γ-ring satisfying the condition aαbβc=aβbαc for all a,b,c∈M, α,β∈Γ, and let D:M→M be an additive mapping such that D(xαx)=D(x)αx+xαd(x) for all x∈M, α∈Γ and for some derivation d of M. We prove that D is a generalized derivation.http://dx.doi.org/10.1155/2012/270132 |
| spellingShingle | Kalyan Kumar Dey Akhil Chandra Paul Isamiddin S. Rakhimov Generalized Derivations in Semiprime Gamma Rings International Journal of Mathematics and Mathematical Sciences |
| title | Generalized Derivations in Semiprime Gamma Rings |
| title_full | Generalized Derivations in Semiprime Gamma Rings |
| title_fullStr | Generalized Derivations in Semiprime Gamma Rings |
| title_full_unstemmed | Generalized Derivations in Semiprime Gamma Rings |
| title_short | Generalized Derivations in Semiprime Gamma Rings |
| title_sort | generalized derivations in semiprime gamma rings |
| url | http://dx.doi.org/10.1155/2012/270132 |
| work_keys_str_mv | AT kalyankumardey generalizedderivationsinsemiprimegammarings AT akhilchandrapaul generalizedderivationsinsemiprimegammarings AT isamiddinsrakhimov generalizedderivationsinsemiprimegammarings |