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Derivations of Lie p-rings with applications on ring extensions and computational methods

  • Bettina Eick
  • Renu Joshi
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Abstract

Derivations are a well-known concept in the theory of Lie algebras. Here we investigate them for Lie p-rings. We show how they apply in the construction of cyclic extensions and in computational methods; in particular, we demonstrate that a consistency test for Lie p-presentations can be facilitated using derivations. The consistency test generalizes inspecific cases to parametrised Lie p-presentations and, further, to the construction of Lie p-covers. These provide a first building block towards a symbolic Lie p-ring generation algorithm.

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Cite

BibTeXRIS
BibTeX
@misc{eick2026derivations,
  title = {{Derivations of Lie $p$-rings with applications on ring extensions and computational methods}},
  author = {Bettina Eick and Renu Joshi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23370},
  eprint = {2610.23370},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23370},
}
RIS
TY  - UNPB
TI  - Derivations of Lie p-rings with applications on ring extensions and computational methods
AU  - Bettina Eick
AU  - Renu Joshi
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23370
UR  - https://arxiv.org/abs/2610.23370
AB  - Derivations are a well-known concept in the theory of Lie algebras. Here we investigate them for Lie p-rings. We show how they apply in the construction of cyclic extensions and in computational methods; in particular, we demonstrate that a consistency test for Lie p-presentations can be facilitated using derivations. The consistency test generalizes inspecific cases to parametrised Lie p-presentations and, further, to the construction of Lie p-covers. These provide a first building block towards a symbolic Lie p-ring generation algorithm.
ER  -