论文标题
在替代环上通勤地图
Commuting maps on alternative rings
论文作者
论文摘要
假设$ \ mathfrak {r} $是$ 2 $，$ 3 $ - torsion免费的unital替代戒指，具有一个idempotent元素$ e_1 $ $ $ \ left（e_2 = 1-e_1 \ right）$，它满足$ x \ mathfrak {r} 1,2 \ right）$。在本文中，我们旨在表征通勤地图。令$φ$为$ \ mathfrak {r} $的通勤地图，因此显示出$φ（x）= zx +ξ（x）$的所有$ x \ in \ mathfrak {r} $，其中$ z \其中$ z \ in \ mathcal {z}（z}（z}（z}）（z}（rathfrak）$ nis $ ins $ ins $ nise $ nistive $ { $ \ mathcal {z}（\ Mathfrak {r}）$。结果，获得了反向通知地图的表征，我们作为应用程序提供了对von Neumann代数相对替代$ c^{*} $的通勤地图的表征 - 没有$ $ i_1 $的中心总和。
Suppose $\mathfrak{R}$ is a $2$,$3$-torsion free unital alternative ring having an idempotent element $e_1$ $\left(e_2 = 1-e_1\right)$ which satisfies $x \mathfrak{R} \cdot e_i = \{0\} \rightarrow x = 0$ $\left(i = 1,2\right)$. In this paper, we aim to characterize the commuting maps. Let $φ$ be a commuting map of $\mathfrak{R}$ so it is shown that $φ(x) = zx + Ξ(x)$ for all $x \in \mathfrak{R}$, where $z \in \mathcal{Z}(\mathfrak{R})$ and $Ξ$ is an additive map from $\mathfrak{R}$ into $\mathcal{Z}(\mathfrak{R})$. As a consequence a characterization of anti-commuting maps is obtained and we provide as an application, a characterization of commuting maps on von Neumann algebras relative alternative $C^{*}$-algebra with no central summands of type $I_1$.
