Generalized Jordan Triple Higher ∗−Derivations on Semiprime Rings
نویسنده
چکیده
Let R be an associative ring not necessarily with identity element. For any x, y ∈ R. Recall that R is prime if xRy = 0 implies x = 0 or y = 0, and is semiprime if xRx = 0 implies x = 0. Given an integer n ≥ 2, R is said to be n−torsion free if for x ∈ R, nx = 0 implies x = 0.An additive mapping d : R → R is called a derivation if d(xy) = d(x)y + yd(x) holds for all x, y ∈ R, and it is called a Jordan derivation if d(x) = d(x)x + xd(x) for all x ∈ R. Every derivation is obviously a Jordan derivation and the converse is in general not true [1, Example 3.2.1]. A classical Herstein theorem [12] shows that any Jordan derivation on a 2-torsion free prime ring is a derivation. Later on Brešar [2] has extended Herstein’s theorem to 2-torsion free semiprime ring. A Jordan triple derivation is an additive mapping d : R → R satisfying
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