Dependent Elements of Derivations on Semiprime Rings
We characterize dependent elements of a commuting derivation d on a semiprime ring R and investigate a decomposition of R using dependent elements of d. We show that there exist ideals U and V of R such that U⊕V is an essential ideal of R, U∩V={0}, d=0 on U, d(V)⊆V, and d acts freely on V.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/696737 |
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| _version_ | 1832562559196069888 |
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| author | Faisal Ali Muhammad Anwar Chaudhry |
| author_facet | Faisal Ali Muhammad Anwar Chaudhry |
| author_sort | Faisal Ali |
| collection | DOAJ |
| description | We characterize dependent elements of a commuting derivation d on a semiprime ring R and investigate a decomposition of R using dependent elements of d. We show that there exist ideals U and V of R such that U⊕V is an essential ideal of R, U∩V={0}, d=0 on U, d(V)⊆V, and d acts freely on V. |
| format | Article |
| id | doaj-art-bcdc3ccaf5134f0faead33c9cf3186af |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bcdc3ccaf5134f0faead33c9cf3186af2025-02-03T01:22:24ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/696737696737Dependent Elements of Derivations on Semiprime RingsFaisal Ali0Muhammad Anwar Chaudhry1Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, PakistanCentre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, PakistanWe characterize dependent elements of a commuting derivation d on a semiprime ring R and investigate a decomposition of R using dependent elements of d. We show that there exist ideals U and V of R such that U⊕V is an essential ideal of R, U∩V={0}, d=0 on U, d(V)⊆V, and d acts freely on V.http://dx.doi.org/10.1155/2009/696737 |
| spellingShingle | Faisal Ali Muhammad Anwar Chaudhry Dependent Elements of Derivations on Semiprime Rings International Journal of Mathematics and Mathematical Sciences |
| title | Dependent Elements of Derivations on Semiprime Rings |
| title_full | Dependent Elements of Derivations on Semiprime Rings |
| title_fullStr | Dependent Elements of Derivations on Semiprime Rings |
| title_full_unstemmed | Dependent Elements of Derivations on Semiprime Rings |
| title_short | Dependent Elements of Derivations on Semiprime Rings |
| title_sort | dependent elements of derivations on semiprime rings |
| url | http://dx.doi.org/10.1155/2009/696737 |
| work_keys_str_mv | AT faisalali dependentelementsofderivationsonsemiprimerings AT muhammadanwarchaudhry dependentelementsofderivationsonsemiprimerings |