RINGS WITH A DERIVATION WHOSE IMAGE IS CONTAINED IN THE NUCLEI

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.25.1994.4458

Keywords:

Nonassociative ring, nucleus, derivation, 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. Suh [4] proved that if $R$ is a prime ring with a derivation dsuch that $d(R) \subseteq G$ then either $R$ is associative or $d^3 =0$. We improve this result by concluding that either $R$ is associative or $d^2 =2d =0$ under the weaker hypothesis $d(R)\subseteq N$\cap M$ or $d(R)\subseteq N\cap M$ or $d(R)\subseteq M\cap L$. Using our result, we obtain the theorems of Posner [3] and Yen [11] for the prime nonassociative rings. In our recent papers we partially generalize the above main result.

References

E. Kleinfeld, "A class of rings which are very nearly associative," Am er. Math. Monthly, 93(1986), 720-722.

P.H . Lee and T. K. Lee, "Note on nilpotent derivations," Proc. Amer. Math. Soc. 98(1986), 31-32.

E. C. Posner, "Derivations in prime rings," Proc. Amer. Math. Soc. 8(1957), 1093-1.100.

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 associators in the left and middle nucleus," Tamkang J. Math. 23(1992), 363-369.

C. T. Yen, "Rings with associators in the left and right nucleus," unpublished manuscript.

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

C. T. Yen, "Rings with a derivation whose some power image is contained in the nuclei," submitted.

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

C. T. Yen, "Rings with a derivation whose image is zero on the associators," to appear in Tamkang J. Math.

C. T. Yen, "On a subring of prime ring with derivation," submitted.

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Published

1994-12-01

How to Cite

YEN, C.-T. (1994). RINGS WITH A DERIVATION WHOSE IMAGE IS CONTAINED IN THE NUCLEI. Tamkang Journal of Mathematics, 25(4), 301-307. https://doi.org/10.5556/j.tkjm.25.1994.4458

Issue

Section

Papers