论文标题
带有iDempotents的Unital Rings的乘法广义Jordan $ n $ derivations
Multiplicative generalized Jordan $n$-derivations of unital rings with idempotents
论文作者
论文摘要
令$ \ mathfrak {a} $为具有非平凡的愿望的Unital环。在本文中，可以证明在某些条件下，每个乘法概括的jordan $ n $ derivation $δ：\ mathfrak {a} \ rightarrow \ mathfrak {a} $都是加性的。更准确地说，证明$δ$是$δ（t）=μt+δ（t）的形式，其中$μ\ in \ mathcal {z}（\ mathfrak {a}）$和$δ：\ m mathfrak {a} \ rightArlow \ rightArrow \ mathfrak \ mathfrak {a}然后将主要结果应用于一些具有非平凡式构造的Unital环的示例，例如三角环，矩阵环，质子环，巢代数，标准操作员代数和冯·诺伊曼代数。
Let $\mathfrak{A}$ be a unital ring with a nontrivial idempotent. In this paper, it is shown that under certain conditions every multiplicative generalized Jordan $n$-derivation $Δ:\mathfrak{A}\rightarrow\mathfrak{A}$ is additive. More precisely, it is proved that $Δ$ is of the form $Δ(t)=μt+δ(t),$ where $μ\in\mathcal{Z}(\mathfrak{A})$ and $δ:\mathfrak{A}\rightarrow\mathfrak{A}$ is a Jordan $n$-derivation. The main result is then applied to some classical examples of unital rings with nontrivial idempotents such as triangular rings, matrix rings, prime rings, nest algebras, standard operator algebras, and von Neumann algebras.
