Rings with generalized commutators in the nuclei

Authors

  • Chen-Te Yen

DOI:

https://doi.org/10.5556/j.tkjm.33.2002.286

Abstract

Let $ R$ be a prime weakly Novikov ring and $ T_k=\underbrace{[[[\ldots[[R,R],R]\ldots,R],R],R]}_{k R's}$ where $ k$ is a positive integer. We prove that if $ T_k\subseteq N_l\cap N_r$ or $ T_k\subseteq N_m\cap N_r$ then $ R$ is associative or $ T_k=0$. Moreover, if $ T_k$ is contained in two of the three nuclei, and $ k=2$ or $ k=3$ then the same conclusions hold. We also consider such rings with derivations. Some similar results of weakly M-rings are obtained.

Author Biography

Chen-Te Yen

Department of Mathematics, Chung Yuan Christian University, Chung Li, Taiwan, 320, Republic of China.

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Published

2002-12-31

How to Cite

Yen, C.-T. (2002). Rings with generalized commutators in the nuclei. Tamkang Journal of Mathematics, 33(4), 371-378. https://doi.org/10.5556/j.tkjm.33.2002.286

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Section

Papers