On pre-Lie rings related to some non-Lazard braces
A Smoktunowicz - arXiv preprint arXiv:2410.05924, 2024 - arxiv.org
Let A be a brace of cardinality $ p^{n} $ for some prime number $ p $. Suppose that either (i)
the additive group of brace $ A $ has rank smaller than $ p-3$, or (ii) $ A^{\frac {p-1} …
the additive group of brace $ A $ has rank smaller than $ p-3$, or (ii) $ A^{\frac {p-1} …
On some connections between braces and pre-Lie rings outside of the context of Lazard's correspondence
A Smoktunowicz - arXiv preprint arXiv:2410.20440, 2024 - arxiv.org
Let $ p> 3$ be a prime number and let $ A $ be a brace whose additive group is a direct sum
of cyclic groups of cardinalities larger than $ p^{\alpha} $ for some $\alpha $. Suppose that …
of cyclic groups of cardinalities larger than $ p^{\alpha} $ for some $\alpha $. Suppose that …
A note on right-nil and strong-nil skew braces
A Ballester-Bolinches, M Ferrara… - arXiv preprint arXiv …, 2023 - arxiv.org
The aim of this short note is to completely answer Questions 2.34 and 2.35 of arXiv:
1806.01127. In particular, we show that a finite strong-nil skew brace $ B $ of abelian type …
1806.01127. In particular, we show that a finite strong-nil skew brace $ B $ of abelian type …
Finite skew braces of square-free order and supersolubility
A Ballester-Bolinches, R Esteban-Romero… - Forum of Mathematics …, 2024 - cambridge.org
The aim of this paper is to study supersoluble skew braces, a class of skew braces that
encompasses all finite skew braces of square-free order. It turns out that finite supersoluble …
encompasses all finite skew braces of square-free order. It turns out that finite supersoluble …
[HTML][HTML] On the structure of left braces satisfying the minimal condition for subbraces
A Ballester-Bolinches, R Esteban-Romero… - Journal of Algebra, 2025 - Elsevier
We analyse the structure of infinite weakly soluble left braces that satisfy the minimal
condition for subbraces. We observe that they can be characterised as the left braces with …
condition for subbraces. We observe that they can be characterised as the left braces with …
On left braces in which every subbrace is an ideal
A Ballester-Bolinches, R Esteban-Romero… - Results in …, 2025 - Springer
The aim of this paper is to introduce and study the class of all left braces in which every
subbrace is an ideal. We call them Dedekind left braces. It is proved that every finite …
subbrace is an ideal. We call them Dedekind left braces. It is proved that every finite …