RINGS WITH A DERIVATION WHOSE IMAGE IS ZERO ON THE ASSOCIATORS

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CHEN-TE YEN

Abstract




Let $R$ be a nonassociative ring, $N$, $M$, $L$ and $G$ the left nucleus,middle nucleus, right nucleus and nucleus respectively. Assume that $R$ is a ring with a derivation $d$ such that $d((R, R, R)) = 0$. It is shown that if $R$ is a simple ring then either $R$ is associative or $d(N \cap L) = 0$; and if $R$ is a prime ring satisfying $Rd(G) \subseteq N$ and $d(G)R \subseteq L$, or $d(G)R +Rd(G) \subseteq M$ then either $R$ is associative or $d(G) =0$. These partially extend our previous results.




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How to Cite
YEN, C.-T. (1995). RINGS WITH A DERIVATION WHOSE IMAGE IS ZERO ON THE ASSOCIATORS. Tamkang Journal of Mathematics, 26(1), 5–8. https://doi.org/10.5556/j.tkjm.26.1995.4371
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Papers

References

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