A note on a pair of derivations of semiprime rings
We study certain properties of derivations on semiprime rings. The main purpose is to prove the following result: let R be a semiprime ring with center Z(R), and let f, g be derivations of R such that f(x)x+xg(x)∈Z(R) for all x∈R, then f and g are central. As an application, we show that noncommutat...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204302139 |
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| author | Muhammad Anwar Chaudhry A. B. Thaheem |
| author_facet | Muhammad Anwar Chaudhry A. B. Thaheem |
| author_sort | Muhammad Anwar Chaudhry |
| collection | DOAJ |
| description | We study certain properties of derivations on semiprime rings. The main purpose is to prove the following result: let R be a semiprime ring with center Z(R), and let f, g be derivations of R such that f(x)x+xg(x)∈Z(R) for all x∈R, then f and g are central. As an application, we show that noncommutative semisimple Banach algebras do not admit nonzero linear derivations satisfying the above central property. We also show that every skew-centralizing derivation f of a semiprime ring R is skew-commuting. |
| format | Article |
| id | doaj-art-13bb7748b948402aacfa8a3b943fdfb4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-13bb7748b948402aacfa8a3b943fdfb42025-02-03T01:27:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004392097210210.1155/S0161171204302139A note on a pair of derivations of semiprime ringsMuhammad Anwar Chaudhry0A. B. Thaheem1Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaWe study certain properties of derivations on semiprime rings. The main purpose is to prove the following result: let R be a semiprime ring with center Z(R), and let f, g be derivations of R such that f(x)x+xg(x)∈Z(R) for all x∈R, then f and g are central. As an application, we show that noncommutative semisimple Banach algebras do not admit nonzero linear derivations satisfying the above central property. We also show that every skew-centralizing derivation f of a semiprime ring R is skew-commuting.http://dx.doi.org/10.1155/S0161171204302139 |
| spellingShingle | Muhammad Anwar Chaudhry A. B. Thaheem A note on a pair of derivations of semiprime rings International Journal of Mathematics and Mathematical Sciences |
| title | A note on a pair of derivations of semiprime rings |
| title_full | A note on a pair of derivations of semiprime rings |
| title_fullStr | A note on a pair of derivations of semiprime rings |
| title_full_unstemmed | A note on a pair of derivations of semiprime rings |
| title_short | A note on a pair of derivations of semiprime rings |
| title_sort | note on a pair of derivations of semiprime rings |
| url | http://dx.doi.org/10.1155/S0161171204302139 |
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