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ON GENERALIZED(, )- REVERSE DERIVATIONS OF PRIME RINGS | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 52, Issue 2, 2011, Pages 0-0 | ||
| Author | ||
| Anwar Khaleel Faraj | ||
| Abstract | ||
| In this paper we will introduce the concept of (, ) reverse derivation, generalized (, ) reverse derivation and generalized left (, ) derivation. Let R be a 2-torsion free prime ring and U a Lie ideal of R such that u2U, for all uU. The main result of this paper states that if F is a generalized (, ) reverse derivation on R which also acts as a homomorphism or as anti- homomorphism on U, then either d=0 or UZ(R) Further, as an application of this result it is shown that, if every generalized left (, ) derivation on R which also acts as a homomorphism or as anti- homomorphism on U, then either d=0 or UZ(R). | ||
| Keywords | ||
| Lie ideals; prime rings; Left derivation; reverse derivation; left; derivation | ||
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