RINGS WITH A DERIVATION WHOSE IMAGE IS ZERO ON THE ASSOCIATORS

Authors

  • CHEN-TE YEN Department of Mathematics, Chung Yuan University, Chung Li, Taiwan, 320, Republic of China.

DOI:

https://doi.org/10.5556/j.tkjm.26.1995.4371

Keywords:

Nonassociative ring, nucleus, derivation, Lie ideal, d-invariant, semiprime ring, prime ring, simple ring

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.

References

T. I. Suh,"Prime nonassociative rings with a special derivation," Abstracts of papers presented to the Amer. Math. Soc., 14(1993), 284.

C. T. Yen, "Rings with a derivation whose image ts contained in the nuclei," Tamkang J. Math. 25 (1994), 303-309.

C. T. Yen, "Rings with a Jordan derivation whose image is contained in the nuclei or commutative center," submitted.

C. T. Yen, "Prime ring with a derivation whose some power image is contained in the nucleus," submitted.

C. T. Yen, "Nonassoc1ative rings with a special derivation," submitted

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Published

1995-03-01

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