From the 1 of 7 linked papers with an AI index.
7 papers
Chain conditions on skew braces and solutions of the Yang-Baxter Equation
Massimiliano Di Matteo, Ramón Esteban-Romero, Maria Ferrara +1
The paper investigates how maximal and minimal chain conditions on ideals of skew braces relate to solubility and nilpotency, extending Hall‑McLain results, and introduces finitene…
Analogues of Grün's lemma and Baer's theorem for skew left braces
A. Ballester-Bolinches, R. Esteban-Romero, L. A. Kurdachenko +1
We prove in this paper some analogues of the well-known group-theoretical Grün's lemma, stating that in a perfect group the first and the second centre coincide, and Baer's theore…
Representations of finite skew braces
A Ballester-Bolinches, R. Esteban-Romero, P. Pérez-Altarriba
One of the classical open problems in the theory of skew left braces is the study of their representation theory. We propose in this paper a definition of representation of a skew…
Addendum/Corrigendum to "On solubility of skew left braces and solutions of the Yang-Baxter equation"
A. Ballester-Bolinches, R. Esteban-Romero, P. Jiménez-Seral +1
In our previous work: Adv. Math. 455 (2024), no. 109880, solubility of solutions was introduced as an extension of solubility of skew braces in the classification context of non-de…
On left braces in which every subbrace is an ideal II
A. Ballester-Bolinches, R. Esteban-Romero, L. A. Kurdachenko +1
The aim of this paper is to take the study of Dedekind braces, that is, left braces for which every subbrace is an ideal, started in a previous paper, further. Dedekind braces …
On products of abelian skew braces
A. Ballester-Bolinches, R. Esteban-Romero, P. Pérez-Altarriba
The main objective of this paper is to study factorisations of skew left braces through abelian subbraces. We prove a skew brace theoretical analog of the classical Itô's theorem…