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arXiv · 2208.04772

On two-sided skew braces

S. Trappeniers
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Abstract

In order to study two-sided skew braces, we introduce the notion of weakly trivial skew braces. We give a classification of such skew braces and show that they are essential in the study of two-sided skew braces. As an application, we obtain new and generalize known results relating the additive and multiplicative group of two-sided skew braces. Further, we show that two a priori different notions of prime and semi-prime skew braces, as introduced by Konovalov, Smoktunowicz and Vendramin, coincide for two-sided skew braces.

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S. Trappeniers. 2022-08-09. On two-sided skew braces. https://doi.org/10.1016/j.jalgebra.2023.05.003

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