In this paper first we define the notion of Jordan left *-derivation and generalized Jordan left ∗-derivation on a *-ring R and then proved the following: Let n ≥ 1 be a fixed integer and R be an (n + 1)!-torsion free ∗-ring with identity element e. If F, d : R → R are n two additive mappings satisfying F(x^(n+1)) = (x*)^nF(x)+ ∑ (x*)^(n−i)x^id(x) for all x ∈ R, then d is a Jordan left *-derivation and F is a generalized Jordan left *-derivation on R.
On generalized Jordan left *-derivation in rings.
SCUDO, GIOVANNI
2012-01-01
Abstract
In this paper first we define the notion of Jordan left *-derivation and generalized Jordan left ∗-derivation on a *-ring R and then proved the following: Let n ≥ 1 be a fixed integer and R be an (n + 1)!-torsion free ∗-ring with identity element e. If F, d : R → R are n two additive mappings satisfying F(x^(n+1)) = (x*)^nF(x)+ ∑ (x*)^(n−i)x^id(x) for all x ∈ R, then d is a Jordan left *-derivation and F is a generalized Jordan left *-derivation on R.File in questo prodotto:
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