TY - JOUR AU - L. Kong AU - J. Zhang PY - 2022/07/07 Y2 - 2024/03/28 TI - Nonlinear skew commuting maps on $\ast$-rings JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 74 IS - 6 SE - Research articles DO - 10.37863/umzh.v74i6.801 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/801 AB - UDC 512.5Let $\mathcal{R}$ 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 $\mathcal{R}$.As an application, the form of nonlinear skew commuting maps on factors is obtained. ER -