Characterizing homomorphisms, derivations and multipliers in rings with idempotents
Characterizing homomorphisms, derivations and multipliers in rings with idempotents
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DOI：
10.1017/s0308210504001088
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发表时间：
2007-02
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影响因子：
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通讯作者：
M. Brešar
中科院分区：
文献类型：
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作者：
M. Brešar
在某些含有非中心幂等元的环中，我们用同态、导子和乘子在满足某些特殊条件的元素上的作用来刻画它们。例如，我们考虑环$\mathcal{A}$和$\mathcal{B}$之间的加法映射$h$满足$h（x）h（y）h（z）=0$的条件，只要$x，y，z\in\mathcal{A}$使得$xy=yz=0$。作为应用，我们得到了关于局部导子和局部乘子的一些新结果。特别地，我们证明了如果$\mathcal{A}$是一个包含非平凡幂等元的素环，那么从$\mathcal{A}$到它自身的每一个局部导子都是一个导子。
In certain rings containing non-central idempotents we characterize homomorphisms, derivations, and multipliers by their actions on elements satisfying some special conditions. For example, we consider the condition that an additive map $h$ between rings $\mathcal{A}$ and $\mathcal{B}$ satisfies $h(x)h(y)h(z)=0$ whenever $x,y,z\in\mathcal{A}$ are such that $xy=yz=0$. As an application, we obtain some new results on local derivations and local multipliers. In particular, we prove that if $\mathcal{A}$ is a prime ring containing a non-trivial idempotent, then every local derivation from $\mathcal{A}$ into itself is a derivation.