@article{article_1008922, title={On centrally extended Jordan derivations and related maps in rings}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={52}, pages={23–35}, year={2023}, DOI={10.15672/hujms.1008922}, author={Bhushan, Bharat and Sandhu, Gurninder S. and Ali, Shakir and Kumar, Deepak}, keywords={Prime ring, semiprime ring, centrally extended Jordan derivation, involution, centrally extended Jordan *-derivation}, abstract={Let $R$ be a ring and $Z(R)$ be the center of $R.$ The aim of this paper is to define the notions of centrally extended Jordan derivations and centrally extended Jordan $\ast$-derivations, and to prove some results involving these mappings. Precisely, we prove that if a $2$-torsion free noncommutative prime ring $R$ admits a centrally extended Jordan derivation (resp. centrally extended Jordan $\ast$-derivation) $\delta:R\to R$ such that <br />\[ <br />[\delta(x),x]\in Z(R)~~(resp.~~[\delta(x),x^{\ast}]\in Z(R))\text{ for all }x\in R, <br />\] <br /> where $’\ast’$ is an involution on $R,$ then $R$ is an order in a central simple algebra of dimension at most 4 over its center.}, number={1}, publisher={Hacettepe University}