RINGS WITH $(R,R,R)$ AND $((R,R,R),R)$ IN THE LEFT NUCLEUS

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.24.1993.4491

Keywords:

Nonassociative ring, semiprime ring, simple ring

Abstract

Let $R$ be a nonassociative ring, and $N$ the left nucleus. It is shown that if $R$ is a simple ring satisfying $(R,R,R) \subset N$ and $((R,R,R),R) \subset N$ and char $R\neq 2$, then $R$ is associative.

References

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C. T. Yen, "Rings with (x,R,x) and (N+NR,R) in the left nucleus," Tamkang J. Math., 23 (1992), 247-251.

C. T. Yen, "Rings with (x,y,z) +(z,y,x) and (N,R) in the left nucleus," Soochow J. Math., 19 (1993), 253-257.

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

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

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

C. T. Yen, "Rings with (x,y, z) +(z,y, x) and (N +R2, R) in the left nucleus," Chung Yuan J., 21 (1992), 5-10.

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Published

1993-06-01

How to Cite

YEN, C.-T. (1993). RINGS WITH $(R,R,R)$ AND $((R,R,R),R)$ IN THE LEFT NUCLEUS. Tamkang Journal of Mathematics, 24(2), 209-213. https://doi.org/10.5556/j.tkjm.24.1993.4491

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Papers