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arXiv · 1206.4177

Left Derivations and Strong Commutativity Preserving Maps on Semiprime $Γ$-Rings

Xiaowei Xu·Jing Ma·Yuan Zhou
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Abstract

In this paper, firstly as a short note, we prove that a left derivation of a semiprime $Γ$-ring $M$ must map $M$ into its center, which improves a result by Paul and Halder and some results by Asci and Ceran. Also we prove that a semiprime $Γ$-ring with a strong commutativity preserving derivation on itself must be commutative and that a strong commutativity preserving endomorphism on a semiprime $Γ$-ring $M$ must have the form $σ(x)=x+ζ(x)$ where $ζ$ is a map from $M$ into its center, which extends some results by Bell and Daif to semiprime $Γ$-rings.

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BibTeXRIS

Xiaowei Xu, Jing Ma, Yuan Zhou. 2012-06-19. Left Derivations and Strong Commutativity Preserving Maps on Semiprime $Γ$-Rings. https://arxiv.org/abs/1206.4177

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