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PreprintCC BY 4.0arXiv

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 ≥ 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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Cite

BibTeXRIS
BibTeX
@misc{cristo2026jordan,
  title = {{On Jordan nilpotency of index n in group rings}},
  author = {Osnel B. Cristo and Mariana G. Cornelissen and Rodrigo L. Rodrigues},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06587},
  eprint = {2611.06587},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06587},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On Jordan nilpotency of index n in group rings
AU  - Osnel B. Cristo
AU  - Mariana G. Cornelissen
AU  - Rodrigo L. Rodrigues
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06587
UR  - https://arxiv.org/abs/2611.06587
AB  - 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 ≥ 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 $6$.
ER  -