On generalized Jordan \ast-derivations with associated Hochschild \ast-۲-cocycles

In this paper, we introduce the notions of generalized \ast-derivations, generalized Jordan \ast-derivations and Jordan triple \ast-derivations with the associated Hochschild \ast-۲-cocycles and then it is proved that if \mathcal{R} is a prime \ast-ring and f:\mathcal{R} \rightarrow \mathcal{R} is a nonzero generalized \ast-derivation with an associated Hochschild \ast-۲-cocycle \beta, then \mathcal{R} is commutative. Some other results regarding generalized Jordan \ast-derivations are also established.

Keywords:

\ast-derivation , generalized Jordan \ast-derivation , Hochschild \ast-۲-cocycle , \ast-ring , prime (semiprime) ring