A Note on Jordan Triple Higher *-Derivations on Semiprime Rings. (9th April 2014) - Ezzat, O. H.
Abstract : We introduce the following notion. Letℕ 0 be the set of all nonnegative integers and letD = ( d i ) i ∈ ℕ 0 be a family of additive mappings of a *-ring R such thatd 0 = i d R ; D is called a Jordan higher *-derivation (resp., a Jordan higher *-derivation) of R ifd n ( x 2 ) = ∑ i + j = n ‍ d i ( x ) d j ( x * i ) (resp., d n ( x y x ) = ∑ i + j + k = n ‍ d i ( x ) d j ( y * i ) d k ( x * i + j ) ) for allx, y ∈ R and eachn ∈ ℕ 0 . It is shown that the notions of Jordan higher *-derivations and Jordan triple higher *-derivations on a 6-torsion free semiprime *-ring are coincident.