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PreprintarXiv licencearXiv

Near-Rings and Skew Braces

  • Riccardo Aragona
  • Norberto Gavioli
  • Martina Iannaccone
  • Giuseppe Nozzi
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Abstract

This paper provides a deeper analysis of Rump's correspondence between near-rings and skew braces. We show that, under a topological assumption on the structure of a near-ring, Rump's correspondence is invertible and it is always possible to construct an associated skew brace. Furthermore, we provide several examples where this topological assumption is fulfilled in well-known algebraic structures such as the Nottingham group, groups of triangular functions, iterated wreath products of arbitrary groups, and groups of IA-automorphisms of free nilpotent groups.

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Cite

BibTeXRIS
BibTeX
@misc{aragona2026nearrings,
  title = {{Near-Rings and Skew Braces}},
  author = {Riccardo Aragona and Norberto Gavioli and Martina Iannaccone and Giuseppe Nozzi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.04874},
  eprint = {2608.04874},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.04874},
}
RIS
TY  - UNPB
TI  - Near-Rings and Skew Braces
AU  - Riccardo Aragona
AU  - Norberto Gavioli
AU  - Martina Iannaccone
AU  - Giuseppe Nozzi
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2608.04874
UR  - https://arxiv.org/abs/2608.04874
AB  - This paper provides a deeper analysis of Rump's correspondence between near-rings and skew braces. We show that, under a topological assumption on the structure of a near-ring, Rump's correspondence is invertible and it is always possible to construct an associated skew brace. Furthermore, we provide several examples where this topological assumption is fulfilled in well-known algebraic structures such as the Nottingham group, groups of triangular functions, iterated wreath products of arbitrary groups, and groups of IA-automorphisms of free nilpotent groups.
ER  -