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arXiv · 2004.05130

Left centralizers on Lie ideals in prime and semiprime gamma rings

Md Fazlul Hoque·Akhil Chandra Paul
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Abstract

Let $U$ be a Lie ideal of a 2-torsion free prime $\Gamma $-ring $M$ such that $u\alpha u\in U$ for all $u\in U$ and $\alpha \in\Gamma $. If $T:M\rightarrow M$ is an additive mapping satifying the relation $T(u\alpha u)=T(u)\alpha u$ for all $u\in U$ and $\alpha \in\Gamma $, then we prove that $T(u\alpha v)=T(u)\alpha v$ for all $u, v\in U$ and $\alpha \in\Gamma $. Also this result is extended to semiprime $\Gamma $-rings.

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Md Fazlul Hoque, Akhil Chandra Paul. 2020-04-10. Left centralizers on Lie ideals in prime and semiprime gamma rings. https://arxiv.org/abs/2004.05130

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