RINGS WITH $(x,R,x)$ AND $(N +NR,R)$ IN THE LEFT NUCLEUS

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Published: Sep 1, 1992
DOI: https://doi.org/10.5556/j.tkjm.23.1992.4548
Keywords:
Nonassociative ring semiprime ring prime ring

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

Abstract




Let $R$ be a nonassociative ring, $N$ the left nucleus. Assume thatN is a nonzero Lie ideal of $R$. It is shown that if $R$ is a prime ring which satisfies $(x,R,x) \subset N$ and $(NR,R)\subset N$ then $R$ is either associative or commutative.




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How to Cite
YEN, C.-T. (1992). RINGS WITH $(x,R,x)$ AND $(N +NR,R)$ IN THE LEFT NUCLEUS. Tamkang Journal of Mathematics, 23(3), 247–251. https://doi.org/10.5556/j.tkjm.23.1992.4548
Issue
Vol. 23 No. 3 (1992)
Section
Papers
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References

Erwin Kleinfeld, "Rings with (x, y, x) and commutators in the left nucleus," Comm. in Algebra, 16(1988), 2023-2029.

Armin Thedy, "On rings with commutators in the nuclei," Math. Z., 119(1971), 213-218.

Armin Thedy, "On rings satisfying ((a, b, c), d) =O," Proc. Amer. Math. Soc., 29(1971), 250-254.

C. T. Yen,"Rings with (x,y,z)+(z,y,x) and (N+R2,R) in the left nucleus,"unpublished manuscript.