Abstract
In this paper we prove that on a 2-torsion free semiprime ring R every Jordan triple (α,β)-derivation (resp. generalized Jordan triple (α,β)-derivation) on Lie ideal L is an (α,β)-derivation on L (resp. generalized (α,β)-derivation on L)
Highlights
In this paper we prove that on a 2-torsion free semiprime ring R every Jordan triple ( ; )-derivation (resp. generalized Jordan triple ( ; )derivation) on Lie ideal L is an ( ; )-derivation on L (resp. generalized ( ; )derivation on L)
Throughout the present paper R will denote an associative ring with center Z(R)
On the other hand, : R ! R an additive mapping is called a Jordan derivation if x2 = (x) x + x(x) holds for all x 2 R: A famous result due to Herstein [11, Theorem 3.3] shows that a Jordan derivation of a prime ring of characteristic not 2 must be a derivation. This result was extended to 2-torsion free semiprime rings by Cusack [10] and subsequently, by Bresar [7]
Summary
Throughout the present paper R will denote an associative ring with center Z(R). A ring R is n-torsion free, where n > 1 is an integer, in case nx = 0; x 2 R, implies x = 0. In this paper we prove that on a 2-torsion free semiprime ring R every Jordan triple ( ; )-derivation Jordan triple ( ; ) derivations, generalized Jordan triple ( ; ) derivations, Lie ideals.
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