@article{Kong_Zhang_2022, title={Nonlinear skew commuting maps on $\ast$-rings}, volume={74}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/801}, DOI={10.37863/umzh.v74i6.801}, abstractNote={<p>UDC 512.5</p> <p>Let $\mathcal{R}$ be a unital $\ast$-ring with the unit $I$. Assume that $\mathcal{R}$ contains a symmetric idempotent $P$ which satisfies $A{\mathcal{R }P = 0$ implies $A=0$ and $A{\mathcal{R }(I-P) = 0$ implies $A = 0$. In this paper, it is proved that if $\phi\colon\mathcal{R} \rightarrow \mathcal{R}$ is a nonlinear skew commuting map, then there exists an element $Z \in \mathcal{Z}_{S}(\mathcal{R})$ such that $\phi(X) = ZX$ for all $X \in \mathcal{R}$, where $\mathcal{Z}_{S}(\mathcal{R})$ is the symmetric center of $\mathcal{R}$.<br>As an application, the form of nonlinear skew commuting maps on factors is obtained.</p&gt;}, number={6}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Kong, L. and Zhang, J.}, year={2022}, month={Jul.}, pages={826 - 831} }