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arXiv · 2611.06587

On Jordan nilpotency of index n in group rings

Osnel B. Cristo·Mariana G. Cornelissen·Rodrigo L. Rodrigues
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Abstract

Let $RG$ be the group ring of an arbitrary group $G$ over an associative and commutative ring $R$ with identity. In this paper, we provide necessary and sufficient conditions for $RG$ to be Jordan nilpotent of index $n \geq 2$. In particular, we establish a connection between the study of Jordan nilpotency in group rings and the study of Lie nilpotency in these algebras. We also classify the Jordan nilpotency of $RG$, over rings of arbitrary characteristic, up to the index $6$.

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Osnel B. Cristo, Mariana G. Cornelissen, Rodrigo L. Rodrigues. 2026-11-04. On Jordan nilpotency of index n in group rings. https://arxiv.org/abs/2611.06587

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