Generalized Jordan triple derivations associated with Hochschild 2–cocycles of rings

Abstract

In the present work, we introduce the notion of a generalized Jordan triple derivation associated with a Hochschild 2-cocycle, and we prove results which imply under some conditions that every generalized Jordan triple derivation associated with a Hochschild 2-cocycle of a prime ring with characteristic different from 2 is a generalized derivation associated with a Hochschild 2-cocycle.

Generalized Jordan triple derivations associated with Hochschild 2-cocycles in semiprime rings

“…In [3] Ezzat and Nabiel have introduced the notion of generalized Jordan triple derivations associated with Hochschild 2-cocycles. A map G: R −→ W is called a generalized Jordan triple derivation associated with a Hochschild 2-cocycle γ: R×R −→ W if G additive and G(lql) = G(l)ql+lG(q)l+lqG(l)+γ(l, q)l+γ(lq, l) for all l, q ∈ R.…”