RINGS WITH $(R,R,R)$ AND $((R,R,R),R)$ IN THE LEFT NUCLEUS
DOI:
https://doi.org/10.5556/j.tkjm.24.1993.4491Keywords:
Nonassociative ring, semiprime ring, simple ringAbstract
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.
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