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Jordan triple (α,β)-higher ∗-derivations on semiprime rings

Ezzat Osama Hamed

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220213

In this article, we define the following: Let N0 be the set of all nonnegative integers and D=(di)i∈N0 a family of additive mappings of a ∗ -ring R such that d0=idR . D is called a Jordan (α,β) -higher ∗ -derivation (resp. a Jordan triple (α,β) -higher ∗ -derivation) of R if dn(a2)=∑i+j=n di(βj(a))dj(αi(a∗i)) (resp. dn(aba)=∑i+j+k=n di(βj+k(a))dj(βk(αi(b∗i)))dk(αi+j(a∗i+j)) ) for all a,b∈R and each n∈N0 . We show that the two notions of Jordan (α,β) -higher ∗ -derivation and Jordan triple (α,β) -higher ∗ -derivation on a 6-torsion free semiprime ∗ -ring are equivalent.