RINGS WITH A JORDAN DERIVATION WHOSE IMAGE IS CONTAINED IN THE NUCLEI OR COMMUTATIVE CENTER

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.27.1996.4343

Keywords:

Nonassociative ring, nucleus, Jordan derivation, derivation, semiprime ring, prime ring

Abstract

Let $R$ be a nonassociative ring, $N$, $L$ and $G$ the left nucleus, right nucleus and nucleus respectively. It is shown that if $R$ is a prime ring with a Jordan derivation d such that $d(R) \subseteq G$ and $(d^2 R), R) \subseteq N$ or $(d^2(R), R) \subseteq L$ then either $R$ is associative or $2d^2 =0$. Moreover. if $(d(R), R) =0$ then either $R$ is associative and commutative or $2d =0$. We also prove that if $R$ is a prime ring with a derivation $d$ and there exists a fixed positive integer $n$ such that $d^n(R) \subseteq G$ and $(d^n(R), R) =0$ then $R$ is associative and $d^n =0$, or $R$ is associative and commutative, or $d^{2n} = (\frac{(2n)!}{n!})d^n = 0$. This partially generalize the results of [3]. We also obtain some results on prime rings with a derivation satisfying other hypotheses.

References

I. N. Herstein, "Jordan derivations of prime rings," Proc. Amer. Math. Soc., 8(1957), 1104-1110.

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

C. T. Yen, "Rings with a derivation whose image is contained in the nuclei," Tamkang J. Math., 25(1994), 301-307.

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

1997-09-01

How to Cite

YEN, C.-T. (1997). RINGS WITH A JORDAN DERIVATION WHOSE IMAGE IS CONTAINED IN THE NUCLEI OR COMMUTATIVE CENTER. Tamkang Journal of Mathematics, 27(3), 201-208. https://doi.org/10.5556/j.tkjm.27.1996.4343

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Papers