PRIME NONASSOCIATIVE RINGS WITH SKEW DERIVATIONS

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.28.1997.4307

Keywords:

Nucleus, Prime nonassociative ring, Skew derivation, Automorphism.

Abstract

Let $R$ be a prime nonassociative ring, $G$ the nucleus of $R$ and $s$, $t$ be automorphisms of $R$.

(I) Suppose that $\delta$ is an $s$-derivation of $R$ such that $s\delta=\delta s$ and $\lambda$ is an $t$-derivation of $R$. If $\lambda\delta^n=0$ and $\delta^n(R)\subset G$, where $n$ is a fixed positive integer, then $\lambda=0$ or $\delta^{3n-1}=0$.

(II) Assume that $\delta$ and $\lambda$ are derivations of $R$. If there exists a fixed positive integer $n$ such that $\lambda^n\delta=0$, and $\delta(R)\subset G$ or $\lambda^n(R)\subset G$, then $\delta^2= 0$ or $\lambda^{6n-4}= 0$.

References

L. O. Chung and J. Luh, "Nilpotency of derivations II", Proc. Amer. Math. Soc., 91(1984), 357-358.

D. W. Jensen "Nilpotency of derivations in prime rings", Proc. Amer. Math. Soc., 123(1995), 2633-2636.

E. C. Posner, "Derivations in prime rings", Proc. Amer. Math. Soc., 8(1957), 1093-1100.

C. T. Yen "Prime ring with a derivation whose some power image is contained in the nucleus", Soochow J. Math., 21(1995), 475-478.

C. T. Yen, Nonassociative rings with skew derivations and rings with associators in the nuclei, Ph. D. thesis, Taiwan University, 1995.

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Published

1997-12-01

How to Cite

YEN, C.-T. (1997). PRIME NONASSOCIATIVE RINGS WITH SKEW DERIVATIONS. Tamkang Journal of Mathematics, 28(4), 309-312. https://doi.org/10.5556/j.tkjm.28.1997.4307

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Papers